  We presented a general classification scheme for the tripartite $L\times
N\times N$ entangled system under stochastic local operation and classical
communication. The whole classification procedure consists of two correlated
parts: the simultaneous similarity transformation of a commuting matrix pair
into a canonical form and the study of internal symmetry of parameters in the
canonical form. Based on this scheme, a concrete example of entanglement
classification for a $3\times N\times N$ system is given.
