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The Type IIb supernova (SN) 1993J is one of only a few stripped-envelope SNe with a progenitor star identified in pre-explosion images. SN IIb models typically invoke H envelope stripping by mass transfer in a binary system. For the case of SN 1993J, the models suggest that the companion grew to 22 M☼ and became a source of ultraviolet (UV) excess. Located in M81, at a distance of only 3.6 Mpc, SN 1993J offers one of the best opportunities to detect the putative companion and test the progenitor model. Previously published near-UV spectra in 2004 showed evidence for absorption lines consistent with a hot (B2 Ia) star, but the field was crowded and dominated by flux from the SN. Here we present Hubble Space Telescope Cosmic Origins Spectrograph and Wide-Field Camera 3 observations of SN 1993J from 2012, at which point the flux from the SN had faded sufficiently to potentially measure the UV continuum properties from the putative companion. The resulting UV spectrum is consistent with contributions from both a hot B star and the SN, although we cannot rule out line-of-sight coincidences. [ABSTRACT FROM AUTHOR]