  The origin for the upward curvature of the upper critical field ($H_{c2}$)
observed in hydrate cobaltate Na$_{0.35}$CoO$_{2} \cdot y$H$_{2}$O is
investigated based on the microscopic gap equation. It is shown that the
observed upward curvature results from the transition between two different
pairing symmetries that occur on different energy bands. Furthermore, different
pairing symmetries involved in the transition results in different upward
curvatures. By considering transitions among all lowest possible pairing
symmetries, it is found that the transition of the pairing symmetry from s-wave
at low fields to $d_{x^2-y^2}+ id_{xy}$ at high fields is the best fit to the
experimental data. Our results provide an important clue to the understanding
of the superconductivity in hydrate cobaltate.
