  We examine charge correlations and instabilities in the pseudogap phase of
high-$T_c$ cuprates modeled by $d$-density wave ordering. The latter has a gap
symmetry similar to the one observed in the $d$-wave superconductor. We use
$t$-$J$ model to describe the charge correlations in the presence of
electron-phonon interaction. Our finding suggest that the charge instability in
the normal state is dominating at an incommensurate wavevector along (1, 1)
instead of (1, 0) for a realistic interaction parameter. The dominance at the
diagonal wavevector is further enhanced if the coupling between electron and
bond-buckling $B_{1g}$ phonon is incorporated. On the other hand, a dominating
charge-density correlation develops along (1, 0) at an incommensurate
wavevector in the $d$-density wave ordered state, which shows a qualitative
agreement with the experiments. The correlation becomes robust only in the
presence of $B_{1g}$ phonon.
