  We elaborate a systematic way to obtain higher order contributions in the
nonlinear steepest descent method for Riemann-Hilbert problem associated with
homogeneous Painleve II equation. The problem is reformulated as a matrix
factorization problem on two circles and can be solved perturbatively reducing
it to finite systems of algebraic linear equations. The method is applied to
find explicitly long-time asymptotic behaviour for tau function of Painleve II
equation.
