  We report single-crystal neutron diffraction studies on a spinel
antiferromagnet GeCo$_2$O$_4$, which exhibits magnetic order with a trigonal
propagation vector and tetragonal lattice expansion ($c/a\simeq1.001$) below
$T_{\rm N}=21$ K. For this inconsistency between spin and lattice in symmetry,
magnetic Bragg reflections with a tetragonal propagation vector were discovered
below $T_{\rm N}$. We discuss spin and orbital states of Co$^{2+}$ ion
underlying the new magnetic component.
