This is an announcement for the paper "Extractig a basis with fixed block inside a matrix" by Pierre Youssef. Abstract: Given $U$ an $n\times m$ matrix of rank $n$ and $V$ block of columns inside $U$, we consider the problem of extracting a block of columns of rank $n$ which minimize the Hilbert-Schmidt norm of the inverse while preserving the block $V$. This generalizes a previous result of Gluskin-Olevskii, and improves the estimates when given a "good" block $V$. Archive classification: math.FA Submitted from: pierre.youssef@univ-mlv.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1401.6434 or http://arXiv.org/abs/1401.6434