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We discuss the entropy-area relation for the small black holes with highercurvature corrections by using the entropy function formalism and fieldredefinition method. We show that the entropy $S_{BH}$ of small black hole isproportional to its horizon area $A$. In particular we find a universal resultthat $S_{BH}=A/2G$, the ratio is two times of Bekenstein-Hawking entropy-areaformula in many cases of physical interest. In four dimensions, the universalrelation is always true irrespective of the coefficients of the higher-orderterms if the dilaton couplings are the same, which is the case for stringeffective theory, while in five dimensions, the relation again holdsirrespective of the overall coefficient if the higher-order corrections are inthe GB combination. We also discuss how this result generalizes to knownphysically interesting cases with Lovelock correction terms in variousdimensions, and possible implications of the universal relation.

Entropy Function and Universality of Entropy-Area Relation for Small Black Holes