  In this paper we study the following problem: for a given bounded positive
function $f$ on a filtered probability space can we find another function (a
multiplier) $m$, $0\le m\le 1$, such that the function $mf$ is not ``too
small'' but its square function is bounded? We explicitly show how to construct
such multipliers for the usual martingale square function and for so-called
conditional square function. Besides that, we show that for the usual square
function more general statement can be obtained by application of a
non-constructive abstract correction theorem by S. V. Kislyakov.
