  The semi-local convergence analysis of a well defined and efficient two-step
Secant method in Banach spaces is presented in this study. The recurrence
relation technique is used under some weak assumptions. The pertinency of the
assumed method is extended for nonlinear non-differentiable operators. The
convergence theorem is also established to show the existence and uniqueness of
the approximate solution. A numerical illustration is quoted to certify the
theoretical part which shows that the earlier study will fail if the function
is non-differentiable.
