Back-to-back connected asymmetric Schottky diodes having metal-semiconductor-metal (MSM) configuration are often encountered practically in solid state devices and, if the intended ohmic contact exhibits rectifying characteristics, then the extraction of diode parameters such as ideality factor and barrier height from forward Current-Voltage (I-V) plots using conventional methods becomes problematic. In this study, a new approach which predicts extremums in measured current-voltage (IV) graph assuming the dominant transport mechanism to be thermionic emission model, have been proposed. Using the proposed method, the first and second derivatives of the voltage- current function in combination to another previously established theoretical approach resulted in significantly accurate extraction of individual barrier heights of a metal-semiconductor-metal (MSM) junction from single experimental I-V measurement. On the other hand, if individual barrier heights are known, using our proposed method the individual ideality factors for the two back-to-back junctions can be calculated. The proposed method has been validated by analyzing a fabricated FeGa/n-Si/Ag MSM Schottky diode, where, the obtained results from this approach are compared with the other method and the values were found out to be in good agreement with each other.