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. Said card includes preferably stored information relating to a maximum level of amount to which the card can be used without stating PIN code, and information relating to the maximum number of such transactions that can be performed without the card communicating and transferring information of executed transactions to the bank holding the account or similar party, such transactions being registered and stored in the memory circuits of the card with a corresponding reduction of available amount. When the card is used in connection with terminals not communicating on-line with account holding bank or similar, transaction data are stored in the memory circuits of the card as well as in the payment terminal, with available amount being correspondingly reduced, and on insertion into a reading terminal directly connected to account holding bank or similar, transfer of in the card stored transaction data takes place for registration/checkup of booked transactions with said bank or similar.