  We find a class of d=4, N=2 supergravity with $R^2$-interactions that admits
exact BPS black holes. The prepotential contains quadratic, cubic and chiral
curvature-squared terms. Black hole geometry realizes stretched horizon, and
consists of anti-de Sitter, intermediate and outermost flat regions. Mass and
entropy depends on charges and are modified not only by higher curvature terms
but also by quadratic term in the prepotential. Consequently, even for large
charges, entropy is no longer proportional to mass-squared.
