Recently, more and more Global Navigation Satellite Systems satellites are available for observation. Apart from obvious advantages, this brings new challenges in developing efficient computational methods of processing signals obtained from more satellites than to date. From the viewpoint of computation process efficiency, the most critical step is ambiguity resolution. Because of the discrete character of ambiguities, the search procedure is employed to perform this task. The search space dimension significantly impacts a search procedure computational load. The time needed for obtaining a solution raises considerably when the search space dimension is greater. Therefore, the improved version of the well-known concept of searching for a fixed solution in a three-dimensional coordinate domain was proposed and tested. The math model of the proposed approach is presented together with the algorithm of the search procedure. The numerical experiments were designed for simulated and real data. The simulated data has been prepared based on the concept proposed by the authors. This data simulation method is described in detail. The test results confirmed the reduction of the time needed to obtain the results when the proposed method is applied. This advantage over traditional methods unveils in the case of many satellites. Moreover, the real-data test pointed out that using the new approach is beneficial in reducing the computation time also in the case of a few satellites if long sessions are processed.