We consider a visual secret sharing scheme with cyclic access structure for n secret images and n shares, where two consecutive shares decode one secret image. This secret sharing scheme can be constructed by using Droste's method. However the contrast of its scheme is 1/(2n). In this paper, it is shown that for every integer n 4, there exists no construction of such a visual secret sharing scheme having a perfect black reconstruction and contrast at least 1/4. Also for every even integer n 4, a new construction of such a visual sharing scheme that satisfies a slightly weaker condition and has a contrast 1/4 is given.