A method for reducing maximum local specific absorption rate ("SAR") in a magnetic resonance imaging ("MRI") system is disclosed. More specifically, a plurality of candidate radio frequency ("RF") pulses are designed and the manner in which they are applied to a subject is determined such that the maximum local SAR is substantially reduced relative to applying the candidate RF pulse that produces the lowest maximum local SAR alone. Put another way, this "time-multiplexing" of a set of RF pulses that each produce approximately the same excitation pattern yields a lower maximum local SAR than does transmitting the individual RF pulse having the lowest local SAR over many repetition times ("TRs"). A convex optimization method is utilized to determine the manner in which the RF pulses are multiplexed in time such that a substantially lower maximum local SAR is achieved.