In this paper, we propose a method for computing partial singular values and the corresponding singular vectors. PCA (Principal Component Analysis) requires only larger singular values and the corresponding singular vectors. Generally, it is obtained by combining the bisection method and the inverse iteration method. However, there are some input matrices, such as the glued Kimura matrix, for which the inverse iteration method fails. Therefore, the OQDS (Orthogonal QD with Shift) method is adopted in this paper. The OQDS method can compute smaller singular values and the corresponding right singular vectors from a bi–diagonal matrix with high accuracy, in the case that the matrix is not split during the decomposition. However, usually, split occurs. Under split, it is not clear which side of the split the smaller singular values fall on. Therefore, to adopt the OQDS method to the PCA, it is necessary to consider how to deal with split. Thus, in this paper, we propose a new implementation of the OQDS method that is not effected by split. Experiments have confirmed that the method is fast while maintaining reliability.