LetQ be the distribution of the suitably normalized sum of i. i. d.k-dimensional random vectors (k2) and letf be a measurable real valued function of the formf(z
1,...,z
k
)=z
1+r(z
2,...,z
k
), where the measurable functionr fulfills certain regularity conditions. A Berry-Esseen-type inequality is derived for the one-dimensional distributionP=Qf
–1.