  We consider the parity transformation and the consequences of parity
invariance on the $n$-point correlation function of the cosmic shear, or any
other polar (or `spin-2') field. The decomposition of the shear field into E-
and B-modes then yields the result that any correlation function which contains
an odd number of B-mode shear components vanishes for parity-invariant random
shear fields. This result is at variance with some statements in the
literature, and the reasons for this is explained. We argue that the parity
invariance provides a very specific diagnostic of systematic effects in shear
data.
