A novel radio frequency (RF) pulse design method for magnetic resonance imaging (MRI) and an improvement to an existing method that reduces specific absorption rate (SAR) in MRI are presented. The new RF pulse design method, variable rate selective excitation optimal RF pulse design method for parallel transmission (VERSEp), is developed for parallel transmission and aim of the method is to design RF pulses with lowest SAR after SAR reduction with variable rate selective excitation (VERSE) method. This is achieved by modifying the SAR optimal RF pulse deisgn method for parallel transmission. Performance of the VERSEp method is tested by comparing VERSE-SAR reduced SAR of the RF pulses designed with SAR optimal RF pulse design method and VERSE-SAR reduced SAR of the RF pulses designed using VERSEp. In the simulations, SAR reductions up to 47% are obtained. Different aspects of VERSEp are also shown with simulations. The second contribution of this work is an improvement made to an existing constrained VERSE-SAR reduction method. The existing VERSE-SAR reduction method uses a peak RF constaint for SAR reduction. In this work, peak square root power constraint is used instead of peak RF constraint in the VERSE-SAR reduction method. In the simulation results, the SAR of the RF pulses designed using the improved method were compared with SAR of the RF pulses designed using the method before improvement. SAR reductions up to 50% are obtained by using peak square root power constrained SAR reduction instead of peak RF constrained SAR reduction.