The para-unitary (PU) M band filter bank, which can beused for M band decomposition, has many useful properties. In this ppaer, attempts have been made to design and and analyze the linear phase para-unitary (LPPU) M band filter bank, which is appropriate to the image coding application. First, we derive a unified coding gain in terms of the correlation in the band, as well as the energy compaction. And M band filter bank has been designed, maximizing the new coding gain. Then, we analyze the image coding performance of the LPPU M band filter bank, such as the energy compaction, the correlation in the band and the entropy. From the analysis, it is shown that the coding gain for LPPU M band filter bank improves, and the coding gain for the LPPU 4 band filter bank approaches very closely to that for LPPU 8 band filter bank, as the length of the filter increases. This fact is also verified by the coding results on the real images.