Summary: The present paper deals with the orientational anisotropy, in the multiplicative elasto-plastic models with non-zero spin and initial orthotropic anisotropy, under the supposition of small elastic strains, while elastic rotations and plastic deformations are large. A new rate form of the model is derived in the Eulerian setting. The evolution in time for the Cauchy stress, plastic part of deformation, tensorial hardening variables and elastic rotations involves the objective derivatives associated with the same elastic spin. A common plastic spin is allowed in the model as direct consequences that follows from the adopted constitutive framework of finite elasto-plastic materials with isoclinic configurations and internal variables. In this model the orientation of the orthotropy directions are characterized in terms of the Euler angles, which replace the elastic rotations. We provided a constitutive framework valuable for the description of the evolution of the orthotropy orientation during a deformation process whose principal directions are different from the orthotropic axes. Only when the plastic spin is non-vanishing, the orientational anisotropy could develop. We proved that only when there exists an initial orthotropic axis which is orthogonal to the sheet, the rotation of the orthotropic axes remains in plane, i.e. in the plane of the sheet, during a plane deformation process. We investigate the effects of three different analytical expressions for the common plastic spin. We make comparisons with the models and the numerical results already provided in the literature.