  We present a numerical finite size scaling study of the localization length
in long cylinders near the integer quantum Hall transition (IQHT) employing the
Chalker-Coddington network model. Corrections to scaling that decay slowly with
increasing system size make this analysis a very challenging numerical problem.
In this work we develop a novel method of stability analysis that allows for a
better estimate of error bars. Applying the new method we find consistent
results when keeping second (or higher) order terms of the leading irrelevant
scaling field. The knowledge of the associated (negative) irrelevant exponent
$y$ is crucial for a precise determination of other critical exponents,
including multifractal spectra of wave functions. We estimate $|y| > 0.4$,
which is considerably larger than most recently reported values. Within this
approach we obtain the localization length exponent $2.62 \pm 0.06$ confirming
recent results. Our stability analysis has broad applicability to other
observables at IQHT, as well as other critical points where corrections to
scaling are present.
