This chapter studies the problem of finding a locally unique solution of a nonlinear equation. It presents semilocal/local convergence study for the secant-like method. A very important problem in the study of iterative procedures is the convergence domain. In general the convergence domain is small. Therefore, it is important to enlarge the convergence domain without additional hypotheses. Using Lipschitz and center-Lipschitz conditions, the chapter presents semilocal convergence results for the secant-like method. It also discusses the local convergence analysis of the secant-like method with some numerical examples.