Slow deposition in ultrahigh vacuum of cobalt onto a clean (010) surface of the ordered alloy TiAl (the bulk structure is tetragonal of the CuAu I type) produces ultrathin films of Co that contain large numbers of steps and defects, but also large regions that are both epitaxial and pseudomorphic. In these regions, the unit mesh of the Co films in the plane of the film is a rhombus with sides equal to 2.855 \AA{} and an angle between the sides of 89.068\ifmmode^\circ\else\textdegree\fi{}. A quantitative low-energy electron-diffraction intensity analysis shows that the bulk interlayer spacing is 1.40\ifmmode\pm\else\textpm\fi{}0.03 \AA{} and that the first interlayer spacing is contracted by 8.6%. Strain analysis finds that the equilibrium (i.e., the unstrained) phase of the films is the metastable body-centered-cubic (bcc) modification of Co (lattice parameter 2.83 \AA{}). Thus, the square unit mesh of bcc Co under a tensile strain of 0.9% becomes a rhombus with a consequent contraction of the bulk interlayer spacing by about 0.86%. The close match of the unit meshes in side and angle stabilizes the metastable bcc Co structure for about 15--20 layers. This case is a rarely encountered example of pseudomorphic epitaxy in which the unit mesh of the equilibrium phase of the film differs from the unit mesh of the substrate either by the ratio of the lengths of the sides or by the magnitude of the angle between the sides or both.