This paper aims to simplify the parameters' extraction for the solar cell single diode model and to show that there are many solutions. The proposed algorithm considers many pairs of ideality factor and series resistance. For each pair, it finds the other three corresponding parameters using any three arbitrary points of the I-V curve by simply solving 3X3 linear system of equations. Each set of parameters is used to simulate an I-V curve. The deviation of simulated curve from the experimental one is assessed by calculating the root mean square error (RMSE). Finally, the best set of five parameters is selected according to its smallest RMSE value. A large set of combinations of the five parameters that yield quasi identical I-V curves was obtained. This is well in line with previous studies reporting wide variations in some parameters including unrealistic values. The proposed method was validated with real experimental data, which showed excellent fits to I-V curves measured under various operating conditions. Compared to other methods, the proposed algorithm uses a single I-V curve and does not make any assumptions on the parameters. Moreover, the calculations do not use any slopes and do not depend on specific points of the curve. (C) 2017 Elsevier Ltd. All rights reserved.