A method for authenticating a user of a terminal equipment connected to a communication network, for access from this terminal equipment to a remote service hosted by a server equipment connected to the network. The method includes the following steps, implemented by the server: authenticating the user from credentials; in the event of successful user authentication, authenticating the client equipment from credentials stored in a first memory of the server in association with the user's credentials, including a command to render a first pattern, the command including parameters describing the first pattern and rendering the first pattern received from the client equipment, so-called reference pattern; deciding on authenticating the client equipment according to the evaluated score, a successful authentication being decided when the match score is greater than a predetermined threshold; and following the authentication decision, updating the credentials of the terminal equipment.