This paper first introduces a (k, n)-sharing matrix S-(k,S- n) and its generation algorithm. Mathematical analysis is provided to show its potential for secret image sharing. Combining sharing matrix with image encryption, we further propose a lossless (k, n)-secret image sharing scheme (SMIE-SIS). Only with no less than k shares, all the ciphertext information and security key can be reconstructed, which results in a lossless recovery of original information. This can be proved by the correctness and security analysis. Performance evaluation and security analysis demonstrate that the proposed SMIE-SIS with arbitrary settings of k and n has at least five advantages: 1) it is able to fully recover the original image without any distortion; 2) it has much lower pixel expansion than many existing methods; 3) its computation cost is much lower than the polynomial-based secret image sharing methods; 4) it is able to verify and detect a fake share; and 5) even using the same original image with the same initial settings of parameters, every execution of SMIE-SIS is able to generate completely different secret shares that are unpredictable and non-repetitive. This property offers SMIE-SIS a high level of security to withstand many different attacks.