Mass measurements on (33,34,42,43)Ar were performed using the Penning trap mass spectrometer ISOLTRAP and a newly constructed linear Paul trap. This arrangement allowed us, for the first time, to extend Penning trap mass measurements to nuclides with half-lives below one second ( 33Ar: T(1/2) = 174 ms). A mass accuracy of about 10(-7) (deltam approximately 4 keV) was achieved for all investigated nuclides. The isobaric multiplet mass equation was checked for the A = 33, T = 3/2 quartet and found to be inconsistent with the generally accepted quadratic form.