Method for authenticating a mobile terminal wherein - the terminal connects to an application server of a mobile telecommunication network of an operator of said terminal at the end of a procedure for authenticating said terminal by means of a third-party telecommunication network , in the event of a positive result of the authentication , method wherein: - the authentication procedure performed by an authentication server of the mobile telecommunication network is based on a connection authorisation certificate from the terminal to the application server, - the connection authorisation certificate is generated by the authentication server from network identification data retrieved, during the successful authentication of the terminal on the mobile telecommunication network; method wherein, during the generation of the connection authorisation certificate: - a session for connecting the mobile terminal to the mobile telecommunication network is opened , - the mobile terminal is authenticated by the mobile network, - in the event of positive authentication , a request is emitted to obtain the connection authorisation certificate from the terminal to the authentication server; method wherein, during the authentication procedure : - a record of the connection authorisation certificate in a memory of the terminal is verified , - a connection message is transmitted to the application server from the terminal, said message including said certificate and the identification data retrieved, when the verification is positive, - the authentication server authenticates the terminal at the end of a comparison between the data contained in the connection message and those recorded in a memory of said server; the method being characterised in that the connection authorisation certificate is generated by the authentication server, when the data memory of the terminal includes an empty record or when the result of the comparison is negative , then is transmitted by the authentication server to the mobile terminal and stored by the mobile terminal in the memory . - the terminal connects to an application server of a mobile telecommunication network of an operator of said terminal at the end of a procedure for authenticating said terminal by means of a third-party telecommunication network , in the event of a positive result of the authentication , method wherein: - the authentication procedure performed by an authentication server of the mobile telecommunication network is based on a connection authorisation certificate from the terminal to the application server, - the connection authorisation certificate is generated by the authentication server from network identification data retrieved, during the successful authentication of the terminal on the mobile telecommunication network; - a session for connecting the mobile terminal to the mobile telecommunication network is opened , - the mobile terminal is authenticated by the mobile network, - in the event of positive authentication , a request is emitted to obtain the connection authorisation certificate from the terminal to the authentication server; - a record of the connection authorisation certificate in a memory of the terminal is verified , - a connection message is transmitted to the application server from the terminal, said message including said certificate and the identification data retrieved, when the verification is positive, - the authentication server authenticates the terminal at the end of a comparison between the data contained in the connection message and those recorded in a memory of said server; <EOS>