  We study the phase transition from a $d_{x^2-y^2}$ to $d_{x^2-y^2}+d_{xy}$
superconductor using the tight-binding model of two-dimensional cuprates. As
the temperature is lowered past the critical temperature $T_c$, first a $
d_{x^2-y^2}$ superconducting phase is created. With further reduction of
temperature, the $ d_{x^2-y^2}+d_{xy}$ phase is created at temperature
$T=T_{c1}$. We study the temperature dependencies of the order parameter,
specific heat and spin susceptibility in these mixed-angular-momentum states on
square lattice and on a lattice with orthorhombic distortion. The
above-mentioned phase transitions are identified by two jumps in specific heat
at $T_c$ and $T_{c1}$.
