  We consider a Moyal plane and propose to make the noncommutativity parameter
\Theta^{\mu\nu} bifermionic, i.e., composed of two fermionic (Grassmann odd)
parameters. The Moyal product then contains a finite number of derivatives,
which allows to avoid difficulties of the standard approach. As an example, we
construct a two-dimensional noncommutative field theory model based on the
Moyal product with a bifermionic parameter and show that it has a locally
conserved energy-momentum tensor. The model has no problems with the canonical
quantization and appears to be renormalizable.
