Analysis of photometry data of the Coma Cluster galaxies shows a prominent effect of galaxy alignment with the cluster itself. The effect shows strong dependence on galaxy position within the cluster, galaxy, luminosity, and, to a lesser degree, color. Galaxies also show a tendency to point toward their nearest neighbors. Quantitative analysis of these effects is presented. Independent measurements of position angles in a small subset of data have been performed. Possible spurious causes for anisotropy are discussed, and it is argued that the effect is real. Weak tendencies found by the earlier authors are in agreement with the results reported here. This effect gives strong support to the adiabatic (fragmentation) picture of galaxy and cluster formation.