  We examine the Chern class map ${c}_{1}: {\rm NS}(S)/p{\rm NS}(S) \rightarrow
{\rm H}^{1}(S, \Omega^{1}_{S})$ for an abelian surface $S$ in characteristic $p
\geq 3$, and give a basis of the kernel $c_{1}$ for the superspecial abelian
surface.
