We investigate the relationship between the magnitudes of Forbush decreases (FDs) and solar-geomagnetic characteristics using daily-averaged galactic cosmic ray (GCR) data from Inuvick (INVK) and Magadan (MGDN) neutron monitor (NM) stations to aid in counting the case of GCR flux intensity modulation. The FDs, obtained with an automated new computer software algorithm from daily-averaged GCR data from the IZMIRAN common website: http://cr0.izmiran.ru/common, at INVK (224) and MGDN (229) NM stations, from 1998 to 2002, were used in the present work. The associated solar-geomagnetic parameters of the same time range were obtained from the OMNI website. A statistical analytical method was employed to test the link between FD amplitudes and solar-geomagnetic variables. We observed negative trends in FD-IMF, FD-SWS, FD-Kp, FD-SSN and FD-SI, while a positive relation was indicated in FD-Dst at both stations. All are statistically significant at a 95% confidence level. The results obtained here imply that solar emission characteristics impact the GCR flux intensity modulation.