This correspondence proposes a new algorithm for deriving all pairs of compatible and incompatible states of any incompletely or completely specified sequential machine. The method needs a single step in checking the contents of the closure classes with respect to each pair of distinct states. A working example is given for illustrating the method by hand computation. The algorithm is implemented by a PL/I program and executed by using the incomplete machine of the example as input data on an IBM system 370/Model 158. These demonstrations assure that the algorithm is feasible and efficient for both hand computation and computer execution.