On July 14, 1982 a Forbush decrease event of unprecedented magnitude was observed worldwide in the cosmic ray records up to particle rigidities of several hundred GV. At the same time the recently commissioned underground proportional counter telescope at Mawson, Antarctica, was recording a newly discovered cosmic ray modulation superposed on the Forbush event (Duldig, Jacklyn and Pomerantz 1985; Jacklyn, Duldig and Pomerantz 1987). The presence of the two phenomena led to complication in deriving the spectrum of the Forbush decrease for particle rigidities corresponding to the shallow observing depth. A technique for resolving such difficulties is presented and applied to the July 1982 decrease and the recurrence event 27 days later. The resulting spectral index γ was found to be ≈ −0.9, similar to the results of the extensive analysis of Russian surface and underground data by Kuzmin et al. (1983).