In the traditional method, we use the eigenfunction to replace the Rayleigh quotient method to determine the true natural frequency. When the beam is uniform, you can use the formula to solve the true natural frequency quickly, but the process of solving the nonuniform beam will become extremely diffcult. In this paper, we use the boundary function that satisfies all the boundary conditions, instead of the traditional eigenfunction into Rayleigh quotient, as an alternative. We can skip the cumbersome fourth-order differential function, just use orthogonality into the boundary function to quickly get the error is very small estimate of the natural frequency. Among them, the boundary function is a minimum of four polynomials, can be used to find the first order natural frequency, and k-order boundary function can be used to solve k-3 order natural frequency. Finally, we compare the approximate third order natural frequencies before the solution with the real solution. We find that the error value is very small and also confirms the satisfying upper bound theory.