In a method and magnetic resonance apparatus for determination of radio-frequency pulses, a time-parallel transmission of a radio-frequency pulse influences the transverse magnetization of an object under examination in a specified spatial region. The spatial region is depicted as a vector and approximated by decomposition into a finite number of weighted basis functions of the decomposition. As a result, the length of the approximated vector is less than the length of the original vector. The radio-frequency pulse is determined as a function of the approximated vector. This method can be used to determine a multichannel RF pulse.