  The magnetization plateaux in two dimensionally coupled S=1/2 dimerized
zigzag Heisenberg chains are investigated by means of the bond operator mean
field approximation. In the absence of the interchain coupling, this model is
known to have a plateau at half of the saturation magnetization accompanied by
the spontanuous translational symmetry breakdown. The parameter regime in which
the plateau appears is reproduced well within the present approximation. In the
presence of the interchain coupling, this plateau is shown to be suppressed.
This result is also supported by the numerical diagonalization calculation.
