  We have studied the cubic to tetragonal phase transition in epitaxial
SrTiO$_3$ films under various biaxial strain conditions using synchrotron X-ray
diffraction. Measuring the superlattice peak associated with TiO$_6$ octahedra
rotation in the low temperature tetragonal phase indicates the presence of a
phase transition whose critical temperature is a strong function of strain,
with T$_C$ as much as 50K above the corresponding bulk temperature.
Surprisingly, the lattice constants evolve smoothly through the transition with
no indication of a phase change. This signals an important change in the nature
of the phase transition due to the epitaxy strain and substrate clamping
effect. The internal degrees of freedom (TiO$_6$ rotations) have become
uncoupled from the overall lattice shape.
