  We study the most general Fierz identities for a pair of non-contracted Dirac
matrices both in the standard basis and for chiral spinors. These identities
are useful in building independent effective operators of fermions that involve
derivatives or sextuple and more fields. We apply them to construct independent
effective four-fermion interactions that contain one to three spin-3/2 chiral
fields. These operators could be relevant to physics of higher-spin baryons and
phenomenology of a neutral, massive spin-3/2 particle as a dark matter
candidate.
