<![CDATA[To find the roots of non-linear equations, numerical methods such as Newton-Raphson and Secant are often used when analytical approaches are difficult to apply. However, these methods are relatively slow due to their low convergence order. Iterative methods with higher convergence orders can speed up the process, but they often involve more complicated derivatives. To overcome this, a high derivative-free iterative method was developed using the predictor and corrector approach. This research aims to develop the method, analyze its convergence order, and develop its algorithm. This research is a theoreticalresearch by reviewing the theories related to the problem at hand. The results show that the new method has a convergence order of six, is faster than the Newton-Raphson and Secant methods in solving non-linear equations, and only involves the first derivative. ]]>
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