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This paper studies the bitonic merge sort algorithm which is difficult to get the prospective sorted result for some odd sequence. We develop a new parallel sorting algorithm, increasing CCI (compare and conditionally interchange) operations, derived from the odd merge sort algorithm. The proposed algorithm is based on a divide-and-conquer strategy. First of all, the sequence to be sorted is decomposed in several groups that are sorted in parallel. After that, all groups are merged into a final, sorted sequence. Therefore, any odd bitonic sequence can be correctly sorted with the mended algorithm. Furthermore, the paper analyzes the computational complexity of the new algorithm and compares it with that of other well-known parallel sorting algorithms. It does not increase memory consumption, and keep the same complexity. Analytic results are compared with those of the sequential algorithm and parallel implementations of other sorting algorithms, obtaining that our proposal outperforms the other solutions.