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The currently used value of 4.1±0.2 for the 36A/38Ar isotopic ratio in the Martian atmosphere is reappraised, and a significantly lower ratio is suggested. Previous analyses of noble gases in impact glass from some Martian meteorites demonstrate that large quantities of Martian atmospheric gases were shock-emplaced into these samples. However, several observations indicate that this trapped Martian gas is composed of two components, one atmospheric and one probably from the Martian mantle. These observations include large variations in 36Ar/38Ar during stepwise gas release, variations in the Ar/Kr/Xe elemental ratios among Martian meteorites, and variations in the cosmogenic-corrected, trapped 36Ar/38Ar ratios over 3.5–4.3 among shock glass samples. Uncertainties in applied corrections for cosmogenic Ar cannot explain these variations. By assuming a range of reasonable values for Martian atmospheric and mantle 40Ar/36Ar, the observed 40Ar/36Ar ratios in shock glass are used to correct for the mantle component and to derive a more precise ratio for the atmospheric component. Using this procedure, one obtains an upper limit for Martian atmospheric 36Ar/38Ar of 3.9, and a probable, but poorly defined range for Martian atmospheric 36Ar/38Ar of ∼3.0–3.6. These lower ratios imply that the degree of mass fractionation during Ar loss from Mars' upper atmosphere is considerably larger than that previously calculated.