We have found that the bulge of the large, nearby Sb galaxy NGC 7331 rotates retrograde to its disk. Analysis of spectra in the region of the near-IR Ca II triplet along the major axis shows that, in the radial range between 5" and ~20", the line-of-sight velocity distribution of the absorption lines has two distinct peaks and can be decomposed into a fast-rotating component with {v} / sigma > 3, and a slower rotating, retrograde component with {v} / sigma ~ 1--1.5. The radial surface brightness profile of the counterrotating component follows that of the bulge, obtained from a two-dimensional bulge-disk decomposition of a near-infrared K-band image, while the fast-rotating component follows the disk. At the radius at which the disk starts to dominate, the isophotes change from being considerably boxy to being very disky. Although a number of spiral galaxies have been found that contain cold, counterrotating disks, this is the first galaxy known to have a boxy, probably triaxial, fairly warm, counterrotating component, which is dominating in the central regions. If it is a bar seen end-on, this bar has to be thicker than the disk. We find that NGC 7331, even though it is a fairly early-type spiral, does not have a conventional, corotating bulge. The fact that the inner component is retrograde makes us believe that it was formed from infalling material in either stellar or gaseous form (see, e.g. Balcells & Quinn). Another possibility, however, is that the structure has been there since the formation of the galaxy. In this case, it will be a challenge to explain the large change in orientation of the angular momentum when going outward radially.