We shall show that a two-parameter extended entropy function is characterized
by a functional equation. As a corollary of this result, we obtain that the
Tsallis entropy function is characterized by a functional equation, which is a
different form used in \cite{ST} i.e., in Proposition \ref{prop01} in the
present paper. We also give an interpretation of the functional equation giving
the Tsallis entropy function, in the relation with two non-additive properties
