After a preliminary exchange between the vendor and the purchaser with a view to completing a transaction corresponding to the payment of an amount due to the vendor for a service rendered, information is exchanged only between the purchaser and a telepayment server (T). The purchaser sends the telepayment server information (1) including data relating to the vendor and said amount. The server then authenticates the vendor's identifier (I1) on the basis of the information received and responds by sending the purchaser a message (2) instructing payment of said amount and including at least said amount and the identifier (I1) of the vendor. The purchaser responds by sending the server confidential information (3) enabling payment of said amount, after verification by the purchaser of the identifier (I1) of the vendor.