  We numerically analyse the evolution of the flavor non-singlet $g_{1}$
structure function taking into account the all-order resummation of $\alpha_{s}
ln^{2}x$ terms which is expected to have much stronger effects than the DGLAP
evolution in the small x region. We include a part of the next-to-leading
logarithmic corrections coming from the resummed ``coefficient function'' which
are not considered in the calculation of Bl\"umlein and Vogt to respect the
factorization scheme independence. It is pointed out that the resummed
coefficient function gives unexpectedly large suppression factor over the
experimentally accessible range of x and Q^{2}. This fact implies that the
next-to-leading logarithmic contributions are very important for the $g_{1}$
structure function.
