Reduction of search region in stereo correspondence can increase performances of the matching process, in the context of execution time and accuracy. For an edge-based stereo matching, we establish relationships between the search space and the parameters like relative displacement of edges, disparity under consideration, image resolution, CCD (Charge-Coupled Device) dimension and focal length of the stereo system. Then, we propose a novel matching strategy for the edge-based stereo. Afterward, we develop a fast edge-based stereo algorithm with combination of the obtained matching strategy and a multiresolution technique using Haar wavelet. Considering the conventional multiresolution technique using Haar wavelet, the execution times of our proposed method are decreased between 26% to 47% in the feature matching stage. Moreover, the execution time of the overall algorithms (including feature extraction and feature matching) is decreased between 15% to 20%. Theoretical investigation and experimental results show that our algorithm has a very good performance; therefore this new algorithm is very suitable for fast edge-based stereo applications like stereo robot vision.