Any high-dimensional data arising from practical applications usually contains irrelevant features, which may impact on the performance of existing subspace clustering methods. This paper proposes a novel subspace clustering method, which reconstructs the feature matrix by the means of unsupervised feature selection (UFS) to achieve a better dictionary for subspace clustering (SC). Different from most existing clustering methods, the proposed approach uses a reconstructed feature matrix as the dictionary rather than the original data matrix. As the feature matrix reconstructed by representative features is more discriminative and closer to the ground-truth, it results in improved performance. The corresponding non-convex optimization problem is effectively solved using the half-quadratic and augmented Lagrange multiplier methods. Extensive experiments on four real datasets demonstrate the effectiveness of the proposed method.