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A construction of a new family of distributed space time codes (DSTCs) having full diversity and low maximum likelihood (ML) decoding complexity is provided for the two phase based cooperative diversity protocols of Jing-Hassibi and the recently proposed generalized non-orthogonal amplify and forward (GNAF) protocol of Rajan et al. The salient feature of the proposed DSTCs is that they satisfy the extra constraints imposed by the protocols and are also four-group ML decodable which leads to significant reduction in ML decoding complexity compared to all existing DSTC constructions. Moreover these codes have uniform distribution of power among the relays as well as in time. Also, simulations results indicate that these codes perform better in comparison with the only known DSTC with the same rate and decoding complexity, namely the coordinate interleaved orthogonal design (CIOD). Furthermore, they perform very close to DSTCs from field extensions which have same rate but higher decoding complexity.