AMPTE/IRM satellite data are used to examine characteristics of the ion pressure tensor in the earth's magnetosheath. The eigenvalues and principal axes of the pressure tensor are computed, and the directions of the principal axes are compared to the direction of the independently measured magnetic field B. When the pressure tensor is anisotropic, as is usually the case in the magnetosheath, one of its eigenvalues is observed to be distinguishable from the other two, which are about equal to one another. Thus, the eigenvector associated with the distinguishable eigenvalue defines an axis of symmetry of the pressure tensor. The symmetry axis is generally not parallel to B. New features of the plasma distribution function are revealed by using the actual eigenvalues of the pressure tensor rather than the usual p⊥ and p∥, where ⊥ and ∥ denote directions perpendicular and parallel to B. ¿ American Geophysical Union 1995