  The aim of this work is to show that the Contou-Carr\`{e}re symbol satisfies
the property of Steinberg symbols: $<f,1-f>_{A((t))^\times} = 1$ for all
elements $f,1-f \in A((t))^\times$. Moreover, we offer a cohomological
characterization of the Contou-Carr\`{e}re symbol from the commutator of a
central extension of groups.
