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A modification of the commonly used Price-Rind scheme for lightning flash frequency (LFF), which can be used in calculations with large spatial and time steps, has been developed. If such steps are applied, the exponent in the relationship of LFF as function of convective cloud heights is smaller by a factor of two over land and smaller by one-fourth over the ocean in comparison to the original Price-Rind scheme. The modified version has been implemented in the Climate Model of the Institute of Atmospheric Physics, Russian Academy of Sciences (IAP RAS CM). The results of LFF simulations with the modified scheme agree better with the satellite data than with the original version. In the IAP RAS CM, global warming (cooling) leads to an LFF increase (decrease) in all seasons. The sensitivity of the LFF to surface air temperature changes at the global level is estimated at 10%/K.