  The temperature dependencies of specific heat and spin susceptibility of a
coupled $d_{x^2-y^2} +id_{xy}$ superconductor in the presence of a weak
$d_{xy}$ component are investigated in the tight-binding model (1) on square
lattice and (2) on a lattice with orthorhombic distortion. As the temperature
is lowered past the critical temperature $T_c$, first a less ordered
$d_{x^2-y^2}$ superconductor is created, which changes to a more ordered
$d_{x^2-y^2} +id_{xy}$ superconductor at $T_{c1} (<T_c)$. This manifests in two
second order phase transitions identified by two jumps in specific heat at
$T_c$ and $T_{c1}$. The temperature dependencies of the superconducting
observables exhibit a change from power-law to exponential behavior as
temperature is lowered below $T_{c1}$ and confirm the new phase transition.
