The advances of Graphic Processing Units (GPU) technology and the introduction of CUDA programming model facilitates developing new solutions for sparse and dense linear algebra solvers. Matrix Transpose is an important linear algebra procedure that has deep impact in various computational science and engineering applications. Several factors hinder the expected performance of large matrix transpose on GPU devices. The degradation in performance involves the memory access pattern such as coalesced access in the global memory and bank conflict in the shared memory of streaming multiprocessors within the GPU. In this paper, two matrix transpose algorithms are proposed to alleviate the aforementioned issues of ensuring coalesced access and conflict free bank access. The proposed algorithms have comparable execution times with the NVIDIA SDK bank conflict - free matrix transpose implementation. The main advantage of proposed algorithms is that they eliminate bank conflicts while allocating shared memory exactly equal to the tile size (T x T) of the problem space. However, to the best of our knowledge an extra space of Tx(T+1) needs to be allocated in the published research. We have also applied the proposed transpose algorithm to recursive gaussian implementation of NVIDIA SDK and achieved about 6% improvement in performance.