A Tr-lattice is a finite lattice L with the following property: If L is isomorphic to the lattice of cyclic flats of a matroid M, then M is transversal. Let L be the lattice consisting of six different elements a, b, c, d, 0, 1, such that \(a\vee b=a\vee c=b\vee c=1\), \(a\wedge b=d\), \(a\wedge c=b\wedge c=0\). It is proved that L is a Tr-lattice, while its inverse \((=dual)\) lattice is not.