A non-unitary non-coherent space-time code is proposed based on full diversity quasi-orthogonal space-time block code.This code can make use of the coherent time of the wireless channel as possible as it can.The conclusion that the proposed code can achieve full algebraic diversity is proved in terms of the definition of algebraic diversity.To exploit the quasi-orthogonal structure for simple decoding an iterative decoding algorithm based on EM algorithm is employed to the proposed non-coherent code.Simulation results demonstrate the iterative decoding algorithm can converge fast and it enjoys a favorable performance-complexity tradeoff.