A higher order panel method based on B-spline representation for both the geometry and the velocity potential is developed for the solution of the flow around two-dimensional lifting bodies. Unlike Lee/Kerwin, who placed multiple control points on each panel and solved the overdetermined system of equation by the least square approach, the present method places only as many number of control points as required by the unknowns of the problem. Especially, a null pressure jump Kutta condition at the trailing edge is found to be effective in stabilizing the solution process and in predicting the correct solution. The new approach, is validated to be accurate through comparison with the analytic solution for a 2-D airfoil and to be less time-consuming due to fewer number of panels required than that used in Lee/Kerwin.