In this paper, we formulate symmetry detection for incompletely specified functions as an equation without using cofactor computation and equivalence checking. Based on this equation, a symmetry detection algorithm is proposed. This algorithm can simultaneously find non-equivalence and equivalence symmetries. Experimental results on a set of benchmarks show that our algorithm is indeed very effective in solving symmetry detection problem for incompletely specified functions. Categories and Subject Descriptors: B.6.3 [Design Aids]: Automatic Synthesis, Switching Theory General Terms: Design, Theory