Summary: Let \(X_ 1,...,X_ n\) be i.i.d.r.v.’s with a common density function f and \(X_{(1)}<...<X_{(n)}\)- be associated order statistics. Let \(F^ n_ i\) denote the \(\sigma\)-fields generated by the r.v.’s \(X_{(j)}\), \(1\leq j\leq i-1\), \(i=2,...,n\). Let \(X^ n(t)\), \(t\in [0,1]\), be a process of form \(n^{-1/2}\sum_{i\leq nt}[g(n\Delta X_{(i)},in^{-1})- Eg(n\Delta X_{(i)},in^{-1})]\) where \(\Delta X_{(i)}=X_{(i)}- X_{(i-1)}\), \(1\leq i\leq n\) with \(X_{(0)}=0\) are spacings. Weak convergence of the martingale part of Doob’s decomposition of the semimartingale \(\{X^ n(i/n),F^ n_{i+1}\}\) to the Wiener process is proved.