A new algorithm is proposed for the simulation of sound ray paths in an arbitrary polyhedral room. The proposed algorithm is developed on the basis of an image model algorithm and the coordinate transformation method is adapted for the calculation of the positions of image sources. In using this method, it is unnecessary to memorize the positions of image sources for the calculation of their descendant higher order image sources, and hence the required size of core memory can be reduced. To reduce computation time, the combinations of reflecting walls from which the valid ray paths cannot be obtained are discriminated against, and excluded in the computation of image sources. These modifications improve the computational efficiency in the image model technique, so that the ray paths from the multiple sound sources in an arbitrary polyhedral room can be simulated, even on a personal computer.