In this paper, a new algorithm for indoor localization using WLAN signal strengths is proposed. The objective of the work was to design a simple and efficient indoor positioning algorithm with good accuracy. The proposed algorithm uses the fingerprinting technique as a pre-processing step. The second step is the application of trilateration within the nearest neighbours found during the first step. The paper describes the algorithm, the environment used to test the algorithm and results obtained. The results show that the proposed algorithm has 44% better accuracy compared to basic fingerprinting technique and the accuracy is 73% better compared to basic trilateration technique. The algorithm has been demonstrated to be independent of the propagation environment and works with no knowledge of the positions and the transmit powers of the WLAN access points in the vicinity. Thus, it is a simple and effective indoor positioning scheme.