[en] YBaCo₄O₇ belongs to a new class of geometrically frustrated magnets like the pyrochlores, in which Co spins occupy corners of tetrahedra. The structure can be viewed as an alternating stacking of Kagome and triangular layers. Exactly half of the triangular units of the Kagome plane are capped by Co ions to form columns running perpendicular to the Kagome sheets. Neutron powder diffraction reveals a broad temperature range of diffuse magnetic scattering, followed by long-range magnetic ordering below 110 K. A unique low-temperature magnetic structure simultaneously satisfies an S=0 arrangement in the uncapped triangular units and antiferromagnetic coupling along the columns. A spin reorientation above 30 K tracks the relative strengths of the in-plane and out-of-plane interactions.