In this paper, a simplified approach for implementing QO-STBC is proposed and evaluated with improved performance. It is based on the Hadamard matrix, in which the scheme exploits the Hadamard matrix property to attain full diversity. Hadamard matrix has the characteristic that diagonalizes a quasi-cyclic matrix and consequently, a decoding matrix so that a diagonal matrix which permits linear decoding is achieved. Using quasicyclic matrices in designing QO-STBC systems requires that the codes should be rotated to reasonably separate one code from another such that error floor in the design can be minimized. It will be shown that, orthogonalizing the secondary codes and then imposing the Hadamard criteria of the scheme can be well diagonalized. The results of this simplified approach demonstrate full diversity and better performance than the interference-free QO-STBC. Results show about 4 dB gain with respect to the interference-free QO-STBC scheme and it performs alike with the earlier Hadamard based QO-STBC designed with rotation. These results achieve the consequent mathematical proposition of the Hadamard matrix and its property is also shown in this study.