Abstract: In this study, we examine the problem of sliced inverse regression (SIR), a widely used method for sufficient dimension reduction (SDR). It was designed to find reduced-dimensional versions of multivariate predictors by replacing them with a minimally adequate collection of their linear combinations without loss of information. Recently, regularization methods have been proposed in SIR to incorporate a sparse structure of predictors for better interpretability. However, existing methods consider convex relaxation to bypass the sparsity constraint, which may not lead to the best subset, and particularly tends to include irrelevant variables when predictors are correlated. In this study, we approach sparse SIR as a nonconvex optimization problem and directly tackle the sparsity constraint by establishing the optimal conditions and iteratively solving them by means of the splicing technique. Without employing convex relaxation on the sparsity constraint and the orthogonal constraint, our algorithm exhibits superior empirical merits, as evidenced by extensive numerical studies. Computationally, our algorithm is much faster than the relaxed approach for the natural sparse SIR estimator. Statistically, our algorithm surpasses existing methods in terms of accuracy for central subspace estimation and best subset selection and sustains high performance even with correlated predictors.