Abstract: Two-dimensional equations of second order accuracy with respect to a small parameter of thickness have been derived for a multilayered plate with orthotropic elastic layers. The principal directions of the layer orthotropy are turned around with respect to each other; therefore, the plate can be considered as monoclinic with piecewise constant elasticity moduli. The equations obtained allow one to take into account correctly the transverse shear and compression of the normal. Taking into account the transverse shear is especially important for plates containing rigid and soft layers.