Abstract: The significance of the present research can be attributed to the systematic study of QR algorithm to solve eigenvalues. The main objective is to study how to develop a new method or strategy to find eigenvalues which improve the convergence of QR algorithm. It is observed that in general the QR algorithm succeeds when the matrix is graded downward with hessenberg form. Our future goal is to analyze theoretical proof for the same and find the well balanced input matrix for QR algorithm. This paper will helpful to all new students who want to work on Matrix decomposition problem.