Orthogonal Matching Pursuit (OMP) is the most popular greedy algorithm that has been developed to find a sparse solution vector to an under-determined linear system of equations. OMP follows the projection procedure to identify the indices of the support of the sparse solution vector. This paper shows that the least-squares (LS) procedure can perform better than the projection procedure in this regard. Consequently, a dummy algorithm called OMP-LS is constructed by replacing the projection step in the OMP algorithm by the proposed least-squares step. Simulations show that the proposed LS procedure has a great impact on improving the performance of the OMP algorithm. The structure of the OMP-LS is then modified by incorporating a backtracking step, which has the impact of correcting erroneously estimated indices. Therefore, the modified algorithm is referred to as OMP with correction (OMPc). The simulation results show that OMPc outperforms all the considered algorithms in most scenarios.