The weighted median filter (WMF) is a generalization of the median filter. The WMF is defined by a window and a set of weight coefficients associated with pixel positions in the window. The procedure of the WMF makes an extended sequence of the pixel values in a window with collecting the value repeatedly by the times of the weight coefficient associated with the pixel position. Then it takes the median value of the sequence as an output. In this paper, we propose a more generalized version that has negative weight coefficients. We call it the rank-order based nonlinear differential operator(RONDO). We define negative weight coefficients using the threshold decomposition. The RONDO detects edges in images degraded by impulsive noise effectively. It has also clear selectivity of edge orientation.