The transmission spectrum of Thue-Morse photonic crystals constructed by positive and negative index materials alternately was investigated.The transmittance was calculated by the recursion relations of the transfer matrix elements.Numerical analyses show that a zero-n gap exists in the TM multilayer system.Comparing with the Bragg gap,this gap is less sensitive to the incident angle and the polarization.The position of gap will not change with the order number of the TM sequence.Meanwhile,the field distribution is investigated for completely transparent states.The field distributions are analogous to the lattice structure.