The modified method for shear viscosity measurements of nematic liquid crystals (NLC) oriented by surfaces is described. The main modification is concerned with usage of photoalignment technique for preparation of mono-domain samples with an orientation controlled by a polarization state of the secondary light irradiation. It provides the azimuthal rotation of a sample at any desirable angle. Thus different geometries of shear flows can be realized after filling the measuring cell with a liquid crystal. The method is experimentally approved at investigation of Poiseuille decay flows of 4-pentyl-4-cyanobiphenyl (5CB) through the channels with a rectangular cross section. The proposed construction of the cell with different surface treatment provides measurements of the three principal viscosities coefficients (Miesowicz' viscosities) with additional usage of electric field. A small amount (less than 0.2ml) of a liquid crystal needed for measurements and simple measuring procedure makes the method to be useful for rheological studies of newly synthesised liquid crystal materials.