We propose the concept of a meta-substrate to broaden the bandwidth of left-handed metamaterials. The
meta-substrate, which behaves like an inhomogeneous magnetic substrate, is composed of another kind of
magnetic metamaterials like metallic closed rings. When conventional metamaterial rings are printed on this kind of meta-substrate in a proper way, the interaction of the metamaterials units can be greatly enhanced, yielding an increased bandwidth of negative permeability. An equivalent circuit analytical model is used to quantitatively characterize this phenomenon. Both numerical and experimental demonstrations are carried out, showing good agreement with theoretical predictions.