The cut method for Gussian beam having axisymmetry is discussed in detail and the expssion for the cut factor is defined in this paper. It is shown that when the factor is equal to 0.9, the cutbeam emittance is twice as large as its rootmeansquare (rms) emittance and the factor is only equal to 0.59 if the cutbeam emittance is equal to its rms emittance. The probability function for the fourdimensional new variables are derived and the sample procedures for them are simply described as well．