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

Transforming Rectangles into Squares, with Applications to Strong Colorings