Using surface x-ray diffraction and ab initio calculations we present a model of the BaTiO₃-(001)- (2x1) surface structure, which has not been considered so far. While the crystal is terminated by two TiO2 layers similarly to SrTiO−3(001)-(2x1), we find that one out of two surface layer Ti-atoms resides in a tetragonal pyramidal oxygen environment. This peculiar geometry leads to a metallic and magnetic surface involving local magnetic moments up to 2μ_B in magnitude located at surface Ti and O atoms. Our results are important for the understanding of the intrinsic surface metallicity of insulating oxides in general.