This paper proposes a novel multi-dimensional modulation (MDM) scheme that achieves better performance than conventional modulation without any diversity or coding gain. We exploit the additional degrees of freedom offered by higher dimensional Euclidean space to construct the proposed constellation design. Analytical results are obtained for the exact symbol and bit error performance of the MDM design over Gaussian and Rayleigh fading channels. Through simulation, we compare the error performance of the MDM scheme with conventional orthogonal modulation.