Visual cryptography is a simple method in which secret information can be directly decoded in human visual system without any cryptographic computations. When the secret image is scattered to n random shares(slides), this scheme has some week point such as pixel expansion and contrast degradation. Therefore, it is necessary to reduce the pixel expansion and improve the contrast in recovered image. In this paper, we propose a new construction method for (k, n) visual cryptography using the cumulative matrix. In case k is odd, we can construct the cumulative matrix perfectly. For even k, the contrast of special pair in decoded image can be achieved best by permitting multiple contract. The proposed method is more simple than that of S. Droste`s in construction and the average contrast of decoded image is improved for the most part. Also, we show that the basis matrices depending on the cumulative matrix are able to be applied for the general access structure.