We present a basis selection method for truncated shell-model calculations. In this method, the correlated basis is constructed with the eigenvectors of the Hamiltonian that is diagonalized in each partition of the shell model. A truncation scheme is established by naturally taking the low-lying correlated-basis vectors in different partitions, which is equivalent to the jj-coupling scheme of the shell model when all the correlated-basis vectors are considered. The results are compared with standard shell-model calculations. The convergence properties of the correlated-basis method are discussed.