The potential part of an unsteady, incompressible, viscous flow is treated by means of a boundary integral method. Discretizing the surface of an object in form of panels, imposing inviscid boundary conditions (no flow through wall) and enforcing conservation of circulation leads to a problem which is not uniquely solvable but numerically ill-posed. A new method which is based on the spectral decomposition of the kernel is proposed. This method is shown to overcome the difficulties of the classical approach. Numerical results are presented.