  We discuss the entropy-area relation for the small black holes with higher
curvature corrections by using the entropy function formalism and field
redefinition method. We show that the entropy $S_{BH}$ of small black hole is
proportional to its horizon area $A$. In particular we find a universal result
that $S_{BH}=A/2G$, the ratio is two times of Bekenstein-Hawking entropy-area
formula in many cases of physical interest. In four dimensions, the universal
relation is always true irrespective of the coefficients of the higher-order
terms if the dilaton couplings are the same, which is the case for string
effective theory, while in five dimensions, the relation again holds
irrespective of the overall coefficient if the higher-order corrections are in
the GB combination. We also discuss how this result generalizes to known
physically interesting cases with Lovelock correction terms in various
dimensions, and possible implications of the universal relation.
