This paper discusses a new algorithm to find the root of non-linear transcendental functions. It is found that Regula-Falsi method always gives guaranteed result but slow convergence. However, interpolation based method does not give guaranteed result but faster than Regula-Falsi method. Therefore, the present paper used these two thoughts and developed a new algorithm which has better convergence than Regula-Falsi and guaranteed result. The present proposed algorithm will be useful for finding the real root of real life problems.