An investigation on the possibility of obtaining a negative refractive index behavior in split ring resonators (SRRs) through magneto-electric coupling is presented. We have performed rigorous electromagnetic simulations using a full-wave 3D simulator, and the obtained results have been verified by our experimental realizations and measurements. The results confirm that the increase of magnetoelectric gyrotropic activity inside a bi-anistropic medium can lead to the establishment of backward-wave propagation.