Abstract: When the boundary element method is used to compute the steady flow of groundwater, one of the most difficult problems is the discontinuity of the normal derivative of groundwater head at some bonudary nodes. A multiple nodes method was proposed by Japanese sientists Watamechi Chew et al in 1980, but the trial-and-error procedure is used and the nodal points must be increased in this method.A new method is proposed in this paper which is called "Node-multivalue Method". As compared with preceeding one neither the nodes must be increased nor the trial-and-error proceduce is needed, and a high accuracy could be achieved in this method.