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This paper proposes a Two Minimum ThreeStep Search (2MN3SS) block matching algorithm that improves the estimation accuracy and retains the simplicity of the Three Step Search (3SS) algorithm. Motion estimation using Full Search (FS) algorithm is computationally extensive. Other previously proposed algorithms reduce the computation by limiting the number of search points at the cost of higher distortion in compensated image. Our proposed algorithm requires higher search points but provides better estimation accuracy compared to three other different types of block matching algorithms such as 3SS, NTSS, and 4SS. The experiments performed on night stare images from IR camera show the robustness and better error performance of the proposed approach.