  We consider the consistent deformation of the relativistic quantum mechanics
introducing the noncommutativity of the space-time and preserving the Lorentz
symmetry. The relativistic wave equation describing the spinning particle on
coordinate dependent noncommutative space-time (noncommutative Dirac equation)
is proposed. The fundamental properties of this equation, like the Lorentz
covariance and the continuity equation for the probability density are
verified. To this end using the properties of the star product we derive the
corresponding probability current density and prove its conservation. The
energy-momentum tensor for the free noncommutative spinor field is calculated.
We solve the free noncommutative Dirac equation and show that the standard
energy-momentum dispersion relation remains valid in the noncommutative case.
