A new method for the testing of combinational digital circuits is presented. The method is based on the concept of the ‘index vector’ of a switching function (Gupta 1987), and represents an extension of syndrome testing. A large percentage of syndrome untestable faults are found to be index vector testable. An approach to testing index vector untestable circuits that relies only on the function realized by the circuit and is independent of the circuit topology is presented. The method can be used for the detection of both single and multiple stuck-at faults in a combinational circuit.