The idea of using parallel imaging to shorten the acquisition time by the simultaneous use of multiple receive coils can be adapted for the parallel transmission of a spatially-selective multidimensional RF pulse. As in data acquisition, a multidimensional RF pulse follows a certain k-space trajectory. Shortening this trajectory shortens the pulse duration. The use of multiple transmit coils, each with its own time-dependent waveform and spatial sensitivity, can compensate for the missing parts of the excitation k-space. This results in a maintained spatial definition of the pulse profile, while its duration is reduced. our work introduces the concept of parallel transmission with arbitrarily shaped transmit coils (termed "Transmit SENSE").