Considering the problem of the white pixels in secret images can not be correctly recovered, which is resulted by the OR operation confined in exiting region incrementing visual cryptography schemes, a novel definition of region incrementing visual cryptography based on XOR operation is proposed for the first time. By iterating random-grid-based (k,k) single-secret visual cryptography scheme and combing the property of 0 as the generator of the 0, 1 group, the shares generation algorithm of (k,n) single-secret-sharing scheme using XOR operation is designed, and the secret sharing and recovering procedures for region incrementing scheme are proposed further. For any original secret pixel s, according to the security level, s is reassigned associated with a randomly chosen qualified set Q in the sharing procedure, and then encoded by the proposed (k,n) single-secret-sharing scheme. The recovering procedure is the same as that of the previous schemes. The effectiveness is theoretically verified at last. Experimental results show that the present scheme not only realizes no pixel expansion, but also can obtain the perfect recovery of white pixels when all the shares are stacked.