We compute the absolute Poisson’s ratio and the bending rigidity exponent of a free-standing two-dimensional crystalline membrane embedded into a space of large dimensionality. We demonstrate that, in the regime of anomalous Hooke’s law, the absolute Poisson’s ratio approaches material independent value determined solely by the spatial dimensionality. Also, we find the following expression for the exponent of the bending rigidity. These results cannot be captured by self-consistent screening approximation.