  In this paper, we present a covariant, relativistic noncommutative algebra
which includes two small deformation parameters. Using this algebra, we obtain
a generalized uncertainty principle which predicts a minimal observable length
in measure of space-time distances. Then, we introduce a new representation for
coordinate and momentum operators which leads to a generalized Dirac equation.
The solutions of the generalized Dirac equation for a free particle will be
explicitly obtained. We also obtain the modified fermionic propagator for a
free Dirac particle.
