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Recently, Rey proposed an efficient (2, n) matrix- based secret image sharing (MSIS) scheme based on simple binary matrix operations. However, the threshold property of Rey's (2, n)-MSIS scheme is compromised. Elsheh and Hamza showed a weakness that if the ranks of the singular matrices used in Rey's scheme are not low enough then one can retrieve the secret information from only one shadow image. In this paper, we overcome this weakness. Our new (2, n)-MSIS scheme satisfies the threshold condition, and has low computational complexity for recovery.