This paper presents a low complexity algorithm for the decoding of space-time block codes (STBC) under non-constant module modulation. Simulation results show that in most cases of non-constant module modulation the new algorithm results in more than 50% reduction in computation complexity comparing to the original maximum likelihood algorithm without any loss of BER performance. This paper presents a low complexity algorithm for the decoding of space-time block codes (STBC) under non-constant module modulation. Simulation results show that in most cases of non-constant module modulation the new algorithm results in more than 50% reduction in computation complexity comparing to the original maximum likelihood algorithm without any loss of BER performance.