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Spherical harmonics serve as basis functions on the unit sphere and spherical harmonic transform is required in analysis and processing of signals in the spectral domain. We investigate the possibility of parallel computation of spherical harmonic transform using Compute Unified Device Architecture (CUDA) with no communication between parallel kernels. We identify the parallel components in the widely used spherical harmonic transform method proposed by Driscoll and Healy. We provide the implementation details and compare the computational complexity with the sequential algorithm. For a given bandlimited signal with maximum spherical harmonics degree L, using the O(L) number of parallel processing kernels, we present that the spherical harmonic coefficients can be calculated in O(Llog2L) time as compared to O(L2log2L). For corroboration, we provide the simulation results using CUDA which indicate the reduction in computational complexity.