  In this paper the usual $Z_2$ graded Lie algebra is generalized to a new
form, which may be called $Z_{2,2}$ graded Lie algebra. It is shown that there
exists close connections between the $Z_{2,2}$ graded Lie algebra and
parastatistics, so the $Z_{2,2}$ can be used to study and analyse various
symmetries and supersymmetries of the paraparticle systems.
