A process for managing an electronic transaction with a trader by use of a microprocessor chip card and of a reading terminal able to interact with the card. The card performs a first comparison where it compares a transaction amount with a first threshold value and instigates a bearer authentication procedure when this amount is above the first threshold. When the amount of the transaction is below the first threshold, the chip card performs a second comparison where it compares with a second threshold value an incremented value of a first counter. The first counter being an aggregate of small amounts counter and being successively incremented by values of amounts of transaction in cases where the amounts are below the first threshold. A procedure for authenticating the bearer of the card is instigated by the card depending on the result of this second comparison.