  We prove that the bar construction of an $E_\infty$ algebra forms an
$E_\infty$ algebra. To be more precise, we provide the bar construction of an
algebra over the surjection operad with the structure of a Hopf algebra over
the Barratt-Eccles operad. (The surjection operad and the Barratt-Eccles operad
are classical $E_\infty$ operads.)
