In the point pattern analysis, the study region is generally chosen as a rectangle. Because the variance of the estimation of the K(d) function tends to increase with the distance scale, its maximum is usually less than one-half the length of the shorter side of the rectangle at estimating the K(d) function. In this case, the minimum of edge-corrected weight is proved to be 0.25. Then a new algorithm of edge-corrected weight is proposed in this paper. A number of points are drawn every an identical segment of the edged-corrected circle. The proportion of the number of points in the study region to the number of points in the whole edge-corrected circle, is approximately equal to the edge-corrected weight. Obviously, the larger the number of points is, the more accurate K(d) function calculated with the algorithm is. With respect to the advantage of the algorithm, it can be applicable to estimating the K(d) function when the study region is a rectangle or an arbitrary polygon. Furthermore, as the information of the point events in a rectangle is not enough, the algorithm can permit us to estimate the K(d) function corresponding to the upper limit of the distance scale (i.e. one-half the length of the diagonal of the rectangle).