This paper presents a general convergence theorem for a class of algorithms that minimize continuous functions in \(\mathbb{R}^n\). The authors use this theorem to construct a convergent conjugate direction algorithm for unconstrained minimization of real-valued functions. This algorithm is derived from the Fletcher-Reeves method with a simple modification. Numerical results are provided to illustrate the behavior of the new algorithm. The paper also demonstrates that the convergence of the variable step Newton method and the steepest descent method can be achieved using the same convergence theorem. The authors further discuss the application of the theorem to quasi-Newton methods and a modified version of the Fletcher-Reeves method, showing that these methods satisfy the necessary conditions for convergence. Finally, numerical experiments comparing the Fletcher-Reeves method and the modified method are presented, highlighting the effectiveness of the new algorithm.This paper presents a general convergence theorem for a class of algorithms that minimize continuous functions in \(\mathbb{R}^n\). The authors use this theorem to construct a convergent conjugate direction algorithm for unconstrained minimization of real-valued functions. This algorithm is derived from the Fletcher-Reeves method with a simple modification. Numerical results are provided to illustrate the behavior of the new algorithm. The paper also demonstrates that the convergence of the variable step Newton method and the steepest descent method can be achieved using the same convergence theorem. The authors further discuss the application of the theorem to quasi-Newton methods and a modified version of the Fletcher-Reeves method, showing that these methods satisfy the necessary conditions for convergence. Finally, numerical experiments comparing the Fletcher-Reeves method and the modified method are presented, highlighting the effectiveness of the new algorithm.