Abstract: The invention relates to a payment system utilizing so called “smart cards”, which include a microprocessor attached to the card with associated memory circuits for storage of transactions, and which via a terminal can be supplied an available and for the card holder useable amount. According to the invention, a unique card number for said card, together with a PIN code chosen by the user and registered for the card, are transformed by means of the card microprocessor into a unique and preferably encoded user certificate for each individual card, which is used for verification of the authority of the user.