  In order to overcome the limitations of the original expression of the
probability distribution appearing in literature of Incomplete Statistics, a
new expression of the probability distribution is derived, where the Lagrange
multiplier %B% introduced here is proved to be identical with that introduced
in the second and third choices for the internal energy constraint in Tsallis'
statistics and to be just equal to the physical inverse temperature. It is
expounded that the probability distribution described by the new expression is
invariant through uniform translation of the energy spectrum. Moreover, several
fundamental thermodynamic relations are given and the relationship between the
new and the original expressions of the probability distribution is discussed.
