  It is proved that every singular cardinal $\lambda$ admits a function
$RTS:[\lambda^+]^2\rightarrow[\lambda^+]^2$ that transforms rectangles into
squares. Namely, for every cofinal subsets $A,B$ of $\lambda^+$, there exists a
cofinal subset $C$ of $lambda^+$, such that $RTS[AxB]$ covers CxC.
  When combined with a recent result of Eisworth, this shows that Shelah's
notion of strong coloring $Pr_1(\lambda^+,\lambda^+,\lambda^+,\cf(\lambda))$
coincides with the classical negative partition relation
$\lambda^+\not\rightarrow[\lambda^+]^2_{\lambda^+}$.
