A method for authenticating a user of a terminal equipment (ET1, ET2) connected to a communication network, for access from this terminal equipment to a remote service (Sv) hosted by a server equipment connected to said network, said method comprising the following steps, intended to be implemented by the server equipment: - authentication (E0, E1, E2) of the user from credentials; - in the event of successful user authentication, authenticating the client equipment from credentials (ID-CRP1 1) stored in a first memory of the server equipment in association with the user's credentials, including a command to render a first pattern whose values are randomly selected from a plurality of predetermined values, said command (SC1 1) comprising parameters describing the first pattern, whose values are selected randomly among a plurality of predetermined values, and rendering (R1 1) the first pattern received from the client equipment, so-called reference pattern, said authentication comprising the following substeps: ∘ sending to the client equipment the first pattern rendering execution command; ∘ upon receipt of a response comprising a rendering of the first pattern by the client equipment, comparing with the reference rendering and evaluating a match score; - 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; characterised in that, following the authentication decision, the method comprises a step (E11, E12) of updating the credentials of the terminal equipment, said step comprising, following a failed authentication, deleting the execution command of rendering of the first pattern and the rendering of the first pattern of the first memory and, in the event of successful authentication of the client equipment, replacing the rendering command of the first pattern and the reference rendering stored in the first memory, with a execution command of rendering of a second pattern, distinct from the first pattern and a second pattern rendering. - authentication (E0, E1, E2) of the user from credentials; - in the event of successful user authentication, authenticating the client equipment from credentials (ID-CRP1 1) stored in a first memory of the server equipment in association with the user's credentials, including a command to render a first pattern whose values are randomly selected from a plurality of predetermined values, said command (SC1 1) comprising parameters describing the first pattern, whose values are selected randomly among a plurality of predetermined values, and rendering (R1 1) the first pattern received from the client equipment, so-called reference pattern, said authentication comprising the following substeps: ∘ sending to the client equipment the first pattern rendering execution command; ∘ upon receipt of a response comprising a rendering of the first pattern by the client equipment, comparing with the reference rendering and evaluating a match score; ∘ sending to the client equipment the first pattern rendering execution command; ∘ upon receipt of a response comprising a rendering of the first pattern by the client equipment, comparing with the reference rendering and evaluating a match score; - 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; characterised in that, following the authentication decision, the method comprises a step (E11, E12) of updating the credentials of the terminal equipment, said step comprising, following a failed authentication, deleting the execution command of rendering of the first pattern and the rendering of the first pattern of the first memory and, in the event of successful authentication of the client equipment, replacing the rendering command of the first pattern and the reference rendering stored in the first memory, with a execution command of rendering of a second pattern, distinct from the first pattern and a second pattern rendering.