  This paper presents a modification of Secant method for finding roots of
equations that uses three points for iteration instead of just two. The
development of the mathematical formula to be used in the iteration process is
provided together with the proof of the rate of convergence which is the same
as the rate of convergence of Muller method of root finding. Application
examples are given where it is demonstrated that for equations involving ill
conditioned cases, the proposed method has better convergence characteristics
compared to Newton and Secant methods.
