Prior to the execution of a program contained in a second chip card inserted in a terminal such as a mobile radio telephone terminal, in addition to a first chip card containing data and connected to a telecommunication network to which the terminal is linked, one of the cards is authenticated by the other, or the two cards are authenticated mutually. This double authentication ensures the authenticity of the program for its overall execution in the terminal and the origin of the second card, distributed through conventional channels, for the network operator.