In [1], Ural et al. propose a sufficient condition for a sequence to be a checking sequence for a complete deterministic FSM. The condition is then used in [1] to elaborate a method for generating checking sequences and it is also used in subsequent improved versions of this method published in [2] and [3]. In this correspondence, we present a counter-example which demonstrates that the condition of the theorem is not sufficient, as it does not address all initialization faults, and show what can be added to make it sufficient.