A higher order panel method based on representation for both the geometry and the velocity potential is developed for the analysis of steady flow around marine propellers. The self-influence functions due to the normal dipole and the source are desingularized through the quadratic transformation, and then the singular part is integrated analytically whereas the non-singular part is integrated using Gaussian quadrature. 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. Numerical experiments indicate that the present method is robust and predicts the pressure distribution around lifting bodies with much fewer panels than existing low order panel methods.