  We establish small correlation bounds for the Moebius function and the Walsh
system, answering affirmatively a question posed by G.Kalai [Ka]. The argument
is based on generalizing the approach of Mauduit and Rivat [M-R] in order to
treat Walsh functions of `large weight', while the `small weight' case follows
from recent work due to B.Green [Gr]. The conclusion is an estimate uniform
over the full Walsh system. A similar result also holds for the Liouville
function.
