  We theoretically study the effects of spin-orbit interactions on symmetry of
a Cooper pair in a spin-singlet d-wave superconductor in two-dimension. The
pairing symmetry is analyzed in terms of the anomalous Green's function which
is obtained by solving the Gor'kov equation analytically. A spin-orbit
interaction induces a spin-triplet p-wave pairing correlation in a uniform
superconductor. An odd-frequency spin-triplet s-wave pairing correlation
appears at a surface of such superconductor as a result of breaking inversion
symmetry locally. We also discuss a close relationship among the odd-frequency
pairing correlation, chirality of surface bound states at the zero energy, and
the anomalous proximity effect. The obtained results enable us to design a
superconductor which causes the strong anomalous proximity effect.
