The length of the longest matching between two DNA sequences plays an im portant rule in genomic studies.The exact distribution of longest matching remains unknown especially when both sequences are Markov dependent.In this talk, Finite Markov Chain imbedding (FMCI) technique will be introduced.Using the FMCI technique, the exact distribution of the length of the longest matching between two Markov dependent sequences will be in terms of transition probability matrix of imbedded Markov chain.Numerical results are provided to illustrate the theoretical results.