Nowadays, many bank cards are smart cards (i.e. integrated-circuit cards) based on the EMV specifications for payment systems. This paper specifies how biometric on-card verification can be integrated into EMV debit and credit cards in a backwards-compatible way. The biometric verification does not change the EMV transaction flow outside the cardholder-verification step. The proposed payment system has been prototyped using Java cards and an applet for handwritten signature on-card verification.