The deterministic Landau-Lifshitz-Gilbert equation has been used to investigate the nonlinear dynamics of magnetization and the specific loss power in magnetic nanoparticles with uniaxial anisotropy driven by a rotating magnetic field. We propose a new type of applied field, which is "simultaneously rotating and alternating," i.e., the direction of the rotating external field changes periodically. We show that a more efficient heat generation by magnetic nanoparticles is possible with this new type of applied field and we suggest its possible experimental realization in cancer therapy which requires the enhancement of loss energies.