By considering the famous identity on the convolution of the central 
binomial coefficients
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\sum_{i+j=n} {{2i} \choose i} {{2j} \choose j} = 4^n
\end{displaymath} -->


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in terms of pairs of <IMG
 WIDTH="12" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
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 ALT="$\ell$">-subsets of <IMG
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 ALT="$2\ell$">-sets, we obtain a new bijective proof and new identities that can be seen as refinements.
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