  I investigate the vortex lattice structure of the Ginzburg Landau free energy
for a two component order parameter in the weak-coupling clean-limit when the
field is along the high symmetry axis in a tetragonal crystal. It is shown that
the vortex lattice phase diagram as a function of the Ginzburg Landau free
energy parameters includes phases with a hexagonal, centered rectangular,
rectangular, and square unit cells. It is also shown that the square vortex
lattice has the largest region of stability. The field distribution of the
square vortex lattice near $H_{c2}$ is determined and the application of this
model to Sr$_2$RuO$_4$ is discussed.
