  We introduce a new Weyl-invariant and generally-covariant vector-tensor
theory with higher derivatives. This theory can be induced by extending the
mimetic construction to vector fields of conformal weight four. We demonstrate
that in gauge-invariant variables this novel theory reduces to the
Henneaux-Teitelboim description of the unimodular gravity. Hence, compared with
the standard general relativity, our new higher derivative vector-tensor theory
has only one new global degree of freedom - the cosmological constant. Finally
we discuss potential extensions of this vector-tensor theory.
