[en] The motion of charged particles in a quadrupole magnet field is considered in linear approximation. A new method is used in which two particular solutions for the particle trajectory equation are combined, determined with initial and final particle coordinates, and new parameters are introduced. A new simpler form of the linear transformation coefficient has been obtained. Some methods of graphical determination of parameters of a magnetic quadrupole element and of linear transformation coefficients are found. These values could be used directly or as a good approximation for further calculations. The problem of transformation in the principal diverging plane of the quadrupole magnet is considered