In this note we give a new approach to the rationality problem of some, Cremona transformation. Let k be any field, k(x,y) be the rational function field of two variables over k. Let sigma be t k-automorphism of k(x,y) defined by
sigma(x)= -x(3x-9y-y(2))(3)/(27x+2x(2)+9xy+2xy(2)-y(3))(2), sigma(y)=-(3x+y(2))(3x-9y-y(2))/27x+2x(2)+9xy+2xy(2)-y(3).
Theorem. The fixed field k(x,y)((sigma)) is rational (= purely transcendental) over k. Embodied in a new proof of the above theorem several general guidelines for solving the rationality problem of Cremona transformations, which may be applied elsewhere.