In this paper, a new local matching algorithm, to estimate dense disparity map in stereo vision, consisting of two stages is presented. At the first stage, the reduction of search space is carried out with a high efficiency, i.e. remarkable decrease in the average number of candidates per pixel, with low computational cost and high assurance of retaining the correct answer. This outcome being due to the effective use of multiple radial windows, intensity information, and some usual and new constraints, in a reasonable manner, retains those candidates which satisfy more constraints and especially being more promising to satisfy the implied assumption in using support windows; i.e., the disparity consistency of the window pixels. Such an output from the first stage, while speeding up the final selection of disparity in the second stage due to search space reduction, is also promising a more accurate result due to having more reliable candidates. In the second stage, the weighted window, although not necessarily being the exclusive choice, is employed and examined. The experimental results on the standard stereo benchmarks for the developed algorithm are presented, confirming that the massive computations to obtain more precise matching costs in weighted window is reduced to about 1/11 and the final disparity map is also improved.