We present in this paper a new method to determine the k largest singular values and their corresponding singular vectors for real rectangular matrices A ∈ R ^n×m . Our approach is based on using a block version of the Power Method to compute an k-block SV D decomposition: A _k = U _k ∑ _k V _k ^T , where ∑ _k is a diagonal matrix with the k largest non-negative, monotonically decreasing diagonal σ ₁ ≥ σ ₂ ⋯ ≥ σ _k . U _k and V _k are orthogonal matrices whose columns are the left and right singular vectors of the k largest singular values. This approach is more efficient as there is no need of calculation of all singular values. The QR method is also presented to obtain the SV D decomposition.