We measured the splay (K11) and bend (K33) elastic constants in the nematic phase of a bent-core liquid crystal. In the vicinity of the nematic-isotropic transition temperature K33 is proportional to the square of the order parameter. In the nematic range K11 increases monotonically with decreasing temperature, whereas K33 is practically independent of temperature and is smaller than K11 . K33 exhibits a pretransitional slow divergence toward the transition temperature to the smectic phase and becomes slightly larger than K11. The small K33 is explained on the basis of strong coupling of the bent shape of the molecules with the bend distortion.