A test is made of the hypothesis that companion galaxies in spiral-dominated groups contain an excess positive redshift. The sample of galaxy groups was rigorously selected, from the standpoint of conventional group membership, by Huchra and Geller (1982). The specific advantages of this sample to the hypothesis test are (a) that it was compiled using an unbiased and impersonal selection algorithm, and (b) that it contains a magnitude-limited and accurate redshift compilation. A sample of 196 companion galaxies in 60 groups shows a statistically significant positive redshift relative to the brightest spiral group members. A sample of 62 companions in 21 E/S0-dominated groups shows no such excess. The positive excess redshift reported here is not expected within the framework of conventional dynamical theory. The most probable conventional explanation for the excess of higher redshift companions is contamination of the group sample by interlopers. It is shown that a reasonable assessment of this contamination falls far short of the observed excess.