This is an announcement for the paper "A quantitative version of the commutator theorem for zero trace matrices" by William B. Johnson, Naratuka Ozawa, and Gideon Schechtman. Abstract: Let $A$ be a $m\times m$ complex matrix with zero trace and let $\e>0$. Then there are $m\times m$ matrices $B$ and $C$ such that $A=[B,C]$ and $\|B\|\|C\|\le K_\e m^\e\|A\|$ where $K_\e$ depends only on $\e$. Moreover, the matrix $B$ can be taken to be normal. Archive classification: math.FA Mathematics Subject Classification: 47B47, 15A60 Submitted from: gideon@weizmann.ac.il The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1202.0986 or http://arXiv.org/abs/1202.0986