We studied the combined effect of the pulse or sinusoidal driving voltage and magnetic field on electrical characteristics and ozone production of a dielectric barrier discharge in air. These effects were studied for both polarities of the pulse. We found that the pulse polarity, as well as the magnetic field, affects discharge ozone production only for higher powers. The discharge driven by sinusoidal voltage produces higher ozone concentration than the discharge driven by voltage pulses of negative polarity. The discharge driven by the voltage pulses of negative polarity produces higher ozone concentrations than the discharge driven by positive voltage pulses. Ozone production yield for the voltage pulses of negative polarity is similar to that of sinusoidal driving voltage. For the positive polarity of voltage pulses, the yield is lower. Magnetic field slightly increases the concentration of ozone produced by the discharge and ozone production yield only for the discharge driven by positive voltage pulses. For the discharge driven by the sinusoidal voltage or by the pulses of the negative polarity magnetic field has only small effect on the concentration of ozone produced by the discharge.