The use of Robin boundary conditions as interfacial transmission conditions in nonoverlapping domain decomposition iterative procedures was introduced by P.~L.~Lions and later discussed by a number of authors. In all of these discussions, the weighting of the flux and the trace of the solution were independent of the iterative step number. Recently, Douglas and Huang have considered an extension in which the weighting has depended on the iterative index and proved that an acceleration in the convergence rate similar to that occurring for alternating-direction iteration using a cycle of pseudo-time steps results. Combined methods have received a lot of attention on the study of the boundary value problems of elliptic equation with singularities domain. The objects of this paper are to extend this accelerated procedure to a singularity problem on a sectorial domain. We show that the convergence rate similar to that occurring for alternating-direction iteration results. Also, a combined method and the methodology of weighting parameter can be used to solve a singularity problem.