The numerical solutions of the existing lifting surface theories do not converge at the parabolic wing tip on account of the singularity. The restriction in the existing theories can be removed by using the new integral equation presented by Dr. Hanaoka. In the first reports, employing the new integral equation, the range of validity of propeller lifting surface theory was extended to include the tip of blade, for the case of the steady propeller. Marine propellers operate in non-uniform flow, so the calculation for the unsteady propeller is important. In the second report, calculation is performed for the unsteady propeller, employing the new integral equation. Following facts are revealed by the results of the numerical investigation. (1) Accurate solutions for the hydrodynamic load distribution near the blade tip of unsteady propellers are obtained by the present method. The method is useful for the calculation of cavitation. (2) For the case of an usual propeller, the existing mode function method is valid in wide range up to 0.9 radius. The method is useful for the calculation of unsteady propeller forces. (3) The effect of p ^*≠ p , that is, the effect of non-linearity in the steady theory on the characteristics of the unsteady propeller, is not small except the region near the tip of blade. The effect should not be neglected for the calculation of unsteady propeller forces. (4) A modification of the present method to shorten the computing time, is attempted. There is possibility of further study on the modification.