Most solar flares originate in sunspot groups, where magnetic field changes lead to energy build-up and release. However, few flare-forecasting methods use information of sunspot-group evolution, instead focusing on static point-in-time observations. Here, a new forecast method is presented based upon the 24-hr evolution in McIntosh classification of sunspot groups. Evolution-dependent >C1.0 and >M1.0 flaring rates are found from NOAA-numbered sunspot groups over December 1988 to June 1996 (Solar Cycle 22; SC22) before converting to probabilities assuming Poisson statistics. These flaring probabilities are used to generate operational forecasts for sunspot groups over July 1996 to December 2008 (SC23), with performance studied by verification metrics. Major findings are: i) considering Brier skill score (BSS) for >C1.0 flares, the evolution-dependent McIntosh-Poisson method BSS_evolution=0.09 performs better than the static McIntosh-Poisson method BSS_static= -0.09; ii) low BSS values arise partly from both methods over-forecasting SC23 flares from the SC22 rates, symptomatic of >C1.0 rates in SC23 being on average $\approx$80% of those in SC22 (with >M1.0 being approx 50%); iii) applying a bias-correction factor to reduce the SC22 rates used in forecasting SC23 flares yields modest improvement in skill relative to climatology for both methods BSS_corr_static = 0.09$ and BSS_corr_evolution = 0.20) and improved forecast reliability diagrams.