  An important invariant of a polynomial $f$ is its Jacobian algebra defined by
its partial derivatives. Let $f$ be invariant with respect to the action of a
finite group of diagonal symmetries $G$. We axiomatically define an orbifold
Jacobian $\mathbb{Z}/2\mathbb{Z}$-graded algebra for the pair $(f,G)$ and show
its existence and uniqueness in the case, when $f$ is an invertible polynomial.
In case when $f$ defines an ADE singularity, we illustrate its geometric
meaning.
