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 between 1 -- 1.5. The radial surface brightness profile of the counter-rotating component follows that of the bulge, obtained from a 2-dimensional bulge-disk decomposition of a near-infrared K-band image, while the fast rotating component follows the disk. At the radius where the disk starts to dominate the isophotes change from being considerably boxy to very disky. Although a number of spiral galaxies have been found that contain cold, couter-rotating disks, this is the first galaxy known to have a boxy, probably triaxial, fairly warm, counter-rotating 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, co-rotating 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 (e.g. Balcells & Quinn 1990). 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.

13 pages latex, including 4 figures and 1 B/W plate. Accepted for Astrophysical Journal Letters. Revised version incorporating some small last-minute changes