The M2 factor matrix for twodimensional HermiteGaussian field is proposed. By introducing coupled beams half width and coupled M2 factor, the M2 factor matrix of the mode after being rotated around the propagation axis by some angle has been derived theoretically in the same coordinate. The rules of change of parameters related to M2 factor matrix varying with the modes' rotation angle have been simulated numerically; and the track of M2 factor vectors versus the modes' rotation angle has been given. Calculation results are in good agreement with theoretically derived ones, which proves that by using M2 factor matrix, M2 factors of a HermiteGaussian mode after rotation by a certain angle can be related with those of the same mode before rotation. This method is universally applicable to the beam quality analysis for asymmetric higher Gaussian beams, and is very important in guiding the mesurement of beam quality in practice.