In recent years, the performance of various kinds of electronic devices including mobile phones has improved. Examples of such electronic devices are: a cellular phone equipped with an RF unit that transmits and receives a high-frequency signal, such as a wireless LAN (Local Area Network); a contactless IC (Integrated Circuit) card equipped with an antenna and that transmits and receives data to and from an external reader/writer; and a contactless IC card reader/writer that reads and writes data to and from such a contactless IC card. For example, non-contact IC cards and contactless IC card readers/writers are used in business affairs and are put to wide use in contactless IC-equipped prepaid cards and electronic money systems. In these electronic devices, the communication distance or communicable range of the antenna depends on the material of the antenna substrate, the thickness of the antenna substrate, the shape of the antenna substrate, etc. In recent years, antenna substrates with various shapes are developed to further improve the communication distance or communicable range. As one of these shapes, there is known a rectangular parallelepiped (FIG. 12(a)) that includes a communication area 81, a non-communication area 82, an antenna radiator (not shown) installed in the communication area 81, and a conductive layer 85 installed in the non-communication area 82. The conductive layer 85 is used to transmit and receive signals to and from the external reader/writer via the antenna radiator installed in the communication area 81 (e.g., see Japanese Unexamined Patent Application Publication Nos. 2005-106542 and 2007-314899). In the antenna substrate described above, as shown in FIG. 12(b), the conductive layer 85 (a part of the non-communication area 82) is covered with a peelable insulating layer 83, whereby an area 84 surrounded by the conductive layer 85 and the peelable insulating layer 83 (i.e., an area other than the communication area 81) is provided as an unconnected portion 86. As shown in FIG. 12(b), there is a possibility that the peeled peelable insulating layer 83 (the peeled area 84) is adhered on the antenna radiator installed in the communication area 81 or between the antenna radiator and the conductive layer 85. When the peeled area 84 is adhered on the antenna radiator, the adhesion of the peeled area 84 becomes a factor of deteriorating the communication distance and communicable range. Further, when the peeled area 84 is adhered on the conductive layer 85, this adhered area is not insulated and may be electrically connected with other electronic parts. If such connection is caused, the communication distance and communicable range are sometimes reduced. The peelable insulating layer 83 may be peeled from the conductive layer 85 due to an impact from the outside during the shipment of the antenna substrate and use of the antenna substrate, or due to a difference in thermal expansion coefficient between the peelable insulating layer 83 and the conductive layer 85. Even if the peeled area 84 is not peeled from the conductive layer 85 and an electrical connection therebetween is not caused, there is a problem that the peelable insulating layer 83 sometimes prevents an electrical signal from being transmitted/received between the antenna radiator and the conductive layer 85. The peelable insulating layer 83 and the conductive layer 85, and the antenna radiator installed in the communication area 81 may be connected with each other via a bonding portion 88 shown in FIG. 12(b). Such a bonding portion 88 prevents the electrical connection between the antenna radiator and the conductive layer 85 from being cut off, but cannot be cut off in all cases. When the peeled area 84 is adhered on the antenna radiator, this adhesion prevents an electric field from being generated from the antenna radiator and thus reduces an antenna performance (e.g., the antenna performance may not be improved to a level expected in the antenna substrate). The peeled area 84 also results in a short circuit between the antenna radiator and the conductive layer 85. On the other hand, when the peeled area 84 is adhered on the conductive layer 85, an adhesive property of the peeled area 84 and an adhesive property of the peeled area 84 are poor, so that the peelable insulating layer 83 and the conductive layer 85 are not always separated from each other by applying a pressure from the outside. In this case, when an attempt is made to peel off the peelable insulating layer 83, the peeled area 84 may be peeled, or the peeled area 84 may remain adhered on the conductive layer 85. In this case, there is a problem that the peeled area 84 causes an electric connection between the antenna radiator and the conductive layer 85 to be cut off. Further, in some cases, it is difficult to cut off the bonding portion 88 completely by an ultrasonic wave, the application of a mechanical force, and the like. In this case, it is impossible to ensure a sufficient strength required for the bonding portion 88, which may deteriorate the antenna performance. Further, as shown in FIG. 13, the antenna substrate 100 includes: a non-communication area 101; a conductive layer 102 arranged on the non-communication area 101; an insulating layer 103 arranged on the conductive layer 102; and an antenna radiator (not shown) arranged in the non-communication area 101. The insulating layer 103 is provided so as to surround the antenna radiator and/or the conductive layer 102 and provided on an upper surface of a peelable insulating layer 104 (which is provided so as to surround the antenna radiator and/or the conductive layer 102). The insulating layer 103 and the peelable insulating layer 104 are sequentially arranged in the non-communication area 101. A bonded area 106 provided as a result of adhesion of a part of the insulating layer 103 and the peelable insulating layer 104 is cut off with a boundary line 105 (a border between the insulating layer 103 and the peelable insulating layer 104), and a remaining peeled area 107 is arranged outside of the boundary line 105 (FIG. 13(a)). The peeled area 107 of the antenna substrate 100 is adhered on the antenna radiator in the non-communication area 101. If the peeled area 107 is adhered on the antenna radiator, an electric field is generated from the antenna radiator to reduce the antenna performance of the antenna substrate 100. If the peeled area 107 is adhered on the conductive layer 102, an electric field is generated from the antenna radiator to reduce the antenna performance of the antenna substrate 100.