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A gauge theory of the Lorentz group with a mass-dimension one gauge fieldcoupling to matter of any spin is developed. As a completely new feature the"Vierbein" assuring local gauge invariance enters not as an independentdynamical field, but emerges as a functional of the Lorentz gauge field. Theunderlying geometry of the theory turns out to be a $SO(1,3)$ Banach bundle.The most general action which is renormalizable by power-counting isconstructed in terms of the gauge field and its first derivatives. It containsno higher derivative terms in the gauge field which destroy unitarity in theusual renormalizable $R^2$-theories of gravitation. Finally equivalence of theLorentz gauge field theory coupled to spin zero matter with General Relativityis established

Local Lorentz invariance and a new theory of gravitation equivalent to General Relativity