The standard harmonic balance method (HBM) approaches periodic solutions of a nonlinear oscillator by calculating the amplitudes of harmonics with a given frequency. This method has difficulties in term of convergence when there are different periodic solutions for the same given frequency. This article presents an iteration procedure to calculate frequencies corresponding a given amplitude of the oscillator first harmonic. The higher order harmonic amplitudes are calculated by combining this procedure and HBM. The numerical applications show that this technique can be used to two periodic solutions corresponding to each amplitude of the first harmonic, including the "unstable" solution.