The payment system according to the present invention comprises an electronic payment device (2) and an authentication device (1) connected (3) together; the payment device (1) comprises a bank card reader (27); the authentication device (1) comprises a fingerprint reader (16) and is adapted to make fingerprint comparisons. When the payment device (2) carries out a payment, in addition to the usual operations, it reads user identification information from a bank card (5) associated to the bank card reader (27) and it authenticates the identity of the user carrying this bank card by means of the authentication device (1) connected thereto.