  In the subcritical interval of the Reynolds number 4320\leq R\leq R_c\equiv
5772, the Navier--Stokes equations of the two--dimensional plane Poiseuille
flow are approximated by a 22--dimensional Galerkin representation formed from
eigenfunctions of the Orr--Sommerfeld equation. The resulting dynamical system
is brought into a generalized normal form which is characterized by a
disposable parameter controlling the magnitude of denominators of the normal
form transformation. As rigorously proved, the generalized normal form
decouples into a low--dimensional dominant and a slaved subsystem. {}From the
dominant system the critical amplitude is calculated as a function of the
Reynolds number. As compared with the Landau method, which works down to
R=5300, the phase velocity of the critical mode agrees within 1 per cent; the
critical amplitude is reproduced similarly well except close to the critical
point, where the maximal error is about 16 per cent. We also examine boundary
conditions which partly differ from the usual ones.
