  We present the results of a new perturbation calculation in polymer
statistics which starts from a ground state that already correctly predicts the
long chain length behaviour of the mean square end--to--end distance $\langle
R_N^2 \rangle\ $, namely the solution to the 2~dimensional~(2D) Edwards model.
The $\langle R_N^2 \rangle$ thus calculated is shown to be convergent in $N$,
the number of steps in the chain, in contrast to previous methods which start
from the free random walk solution. This allows us to calculate a new value for
the leading correction--to--scaling exponent~$\Delta$. Writing $\langle R_N^2
\rangle = AN^{2\nu}(1+BN^{-\Delta} + CN^{-1}+...)$, where $\nu = 3/4$ in 2D,
our result shows that $\Delta = 1/2$. This value is also supported by an
analysis of 2D self--avoiding walks on the {\em continuum}.
