  We study bond-order parameters for generalized $t$-$J$ models on a square
lattice. Using the plane-wave limit the considered order parameters form basis
functions for irreducible representations of the symmetry transformations of
the point group and of time reversal. We show that for instability wave vectors
along the diagonals all possible basis functions are either fine-tuned (i.e.,
obey restrictions beyond the requirements of symmetry) or break time reversal
symmetry and thus describe flux states. For instability wave vectors along the
crystalline axes, corresponding to the observed case in underdoped cuprates,
there are only three representations with $A_1$, $B_1$, and $E$ symmetry which
do not break time reversal symmetry in the general case. We suggest that one of
them has recently been observed in resonant elastic X-ray scattering.
