A new method for constructing a checking sequence for finite state machine based testing is introduced. Unlike previous methods, which are based on state recognition using a single state identification sequence, our approach makes use of multiple state identification sequences. Using multiple state identification sequences provides an opportunity to construct shorter checking sequences, choosing greedily the state identification sequence that best suits our goal at different points during the construction of the checking sequence. We present the results of an experimental study showing that our approach produces shorter checking sequences than the previously published methods.