  We propose that the inhomogeneous patterns seen by STM in some underdoped
superconducting cuprates could be related to a bond-order-wave instability of
the staggered flux state, one of the most studied "normal" state proposed to
compete with the d-wave RVB superconductor. A checkerboard pattern is obtained
by a Gutzwiller renormalized mean-field theory of the t-J model for doping
around 1/8. It is found that the charge modulation is always an order of
magnitude smaller than the bond-order modulations. This is confirmed by an
exact optimization of the wavefunction by a variational Monte Carlo scheme. The
numerical estimates of the order parameters are however found to be strongly
reduced w.r.t their mean-field values.
