  We elaborate in this paper a translation-invariant model for fermions in
4-dimensional noncommutative Euclidean space. The construction is done on the
basis of the renormalizable noncommutative translation-invariant Phi4 theory
introduced by R. Gurau et al. We combine our model with the scalar model, in
order to study the noncommutative pseudo-scalar Yukawa theory. After we derive
the Feynman rules of the theory, we perform an explicit calculation of the
quantum corrections at one loop level to the propagators and vertices.
