  The classical and quantum correlations sharing between modes of the Dirac
fields in the noninertial frame are investigated. It is shown that: (i) The
classical correlation for the Dirac fields decreases as the acceleration
increases, which is different from the result of the scalar field that the
classical correlation is independent of the acceleration; (ii) There is no
simple dominating relation between the quantum correlation and entanglement for
the Dirac fields, which is unlike the scalar case where the quantum correlation
is always over and above the entanglement; (iii) As the acceleration increases,
the correlations between modes $I$ and $II$ and between modes $A$ and $II$
increase, but the correlations between modes $A$ and $I$ decrease.
