Abstract: A payment transaction system comprises payment terminals and a distribution centre that can be connected to teh terminal and to a monetary institution of financial establishment. Each payment terminal (11, 12, 13, . . . 1n) has its individual account (111, 121) in said monetary establishment (14, 16) and includes means (112, 122) for reading and sending card numbers to the distribution centre (10) for activating therein a first identity code corresponding to earlier sent card number, means for reading a second identity code (payer fingerprint), and means for opening said individual account (111, 121) in the monetary institution (14, 16) when agreement is found between the activated first identity code and the read second identity code. Each terminal also includes means (113, 123) for making the payment concerned, upon receipt of a balance signal from said individual account (111, 121) in the monetary institution (14, 16). Each payment terminal and the distribution centre include means (101 in FIG.