X m ?is the r-th maximum of {?em class="EmphasisTypeItalic">X k ?1?em class="EmphasisTypeItalic">k?em class="EmphasisTypeItalic">n} and \({}^{(r)}S_{n}=S_{n}-(X_{n}^{(1)}+\cdots +X_{n}^{(r)})\) be the trimmed sums when extreme terms are excluded, where \(S_{n}={\sum }_{k=1}^{n}X_{k}\). In this paper, it is stated that under some suitable conditions, $$\lim _{n\to \infty }\frac {1}{\sqrt {2\log \log n}}\max _{1\le k\le n}\frac {\|^{(r)}S_{k}\|}{\sqrt {k}}=\sigma (X)~~~\mathrm {a.s.},$$" />