A method of payment by means of a payment medium that is capable of communicating remotely with the payment terminal, the payment medium bearing an amount and including a first rewritable memory and a second fuse memory, comprising a plurality of bits (1, 2, 3, 4, 5, 6, 7, 8) each adapted to change its state one single time, characterised in that it comprises the following successive steps: o placing in communication of the payment medium with the payment terminal, with the amount having a value before payment and an image of the value before payment being stored in the first memory, o reading of the first and second memories (34, 36) and o deducing of the value before payment from the data read from the first and second memories (34, 36), and the following steps: o assigning of a value after payment to the amount, which is lower than the value before payment, in replacement of the value before payment, and o changing of the state of at least one bit (6, 7, 8) of the second memory, the or each bit (6, 7, 8) switching from a first state into a second state, when the difference between the values before and after payment is greater than a threshold value, the changing of state causing changing of a range of permissible values for the amount, the deducing step comprising the following sub-steps: o determination of the range of permissible values for the amount, which is a function of the states of the bits (1, 2, 3, 4, 5, 6, 7, 8) of the second memory, o checking (110, 170) the appropriateness of the image of the value before payment (V 1) with respect to the range of permissible values, and o if the image of the value before payment (V 1) is greater than the range of permissible values, refusal of payment, or changing the image of the value before payment (V 1) in order for it to be included within the range of permissible values. o placing in communication of the payment medium with the payment terminal, with the amount having a value before payment and an image of the value before payment being stored in the first memory, o reading of the first and second memories (34, 36) and o deducing of the value before payment from the data read from the first and second memories (34, 36), o assigning of a value after payment to the amount, which is lower than the value before payment, in replacement of the value before payment, and o changing of the state of at least one bit (6, 7, 8) of the second memory, the or each bit (6, 7, 8) switching from a first state into a second state, when the difference between the values before and after payment is greater than a threshold value, the changing of state causing changing of a range of permissible values for the amount, o determination of the range of permissible values for the amount, which is a function of the states of the bits (1, 2, 3, 4, 5, 6, 7, 8) of the second memory, o checking (110, 170) the appropriateness of the image of the value before payment (V 1) with respect to the range of permissible values, and o if the image of the value before payment (V 1) is greater than the range of permissible values, refusal of payment, or changing the image of the value before payment (V 1) in order for it to be included within the range of permissible values.