We study the decay of orientational correlations between segments, the gyration radius, and the Kuhn segment length of a 2D comblike macromolecule (brush) with random distribution of the side chains with respect to the backbone. This distribution is assumed to be fixed and controlled by an initial conformation of the molecule in 3D. Both "frozen" (quenched) fluctuations of left-right positions of the side chains and the thermodynamic fluctuations of the whole molecule in 2D are taken into account. We show that extra bending of the brush due to the locally uneven number of left and right side chains promotes the decay of the orientational correlation function, and reduces the gyration radius. The correlation function has a nonmonotonous decay with one minimum.