Learning-based hashing has recently received considerable attentions due to its capability of supporting efficient storage and retrieval of high-dimensional data such as images, videos, and documents. In R 2 SDH, correntropy is adopted to replace the least square regression (LSR) model in SDH for achieving better robustness. Furthermore, considering the commonly used distance metrics such as cosine and Euclidean distance are invariant to rotational transformation, rotation is integrated into the original zero-one label matrix used in SDH, as additional freedom to promote flexibility without sacrificing accuracy. The rotation matrix is learned through an optimization procedure. Experimental results on three image datasets (MNIST, CIFAR-10, and NUS-WIDE) confirm that R 2 SDH generally outperforms SDH.