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This paper describes a multi-threaded parallel design and implementation of the Smith-Waterman (SW) algorithm on graphic processing units (GPUs) with NVIDIA corporation's Compute Unified Device Architecture (CUDA). Central to this is a divide and conquer approach which divides the computation of a whole pairwise sequence alignment matrix into multiple sub-matrices (or parallelograms) each running efficiently on the available hardware resources of the GPU in hand, with temporary intermediate data stored in global memory. Moreover, we use thread warps and padding techniques in order to decrease the cost of thread synchronization, as well as loop unrolling in order to reduce the cost of conditional branches. While intermediate data is stored in global memory for large queries, the most inner loop in our implementation will only access shared memory and registers. As a result of these optimizations, our implementation of the SW algorithm achieves a throughput ranging between 9.09 GCUPS (Giga Cell Update per Second) and 12.71 GCUPS on a single-GPU version, and a throughput between 29.46 GCUPS and 43.05 GCUPS on a quad-GPU platform. Compared with the best GPU implementation of the SW algorithm reported to date, our implementation achieves up to 46 % improvement in speed. The source code of our implementation is available in the public domain for Bioinformaticians to benefit from its performance.