  Polynomials with all the coefficients in $\{ 0,1\}$ and constant term 1 are
called Newman polynomials, whereas polynomials with all the coefficients in $\{
-1,1\}$ are called Littlewood polynomials. By exploiting an algorithm developed
earlier, we determine the set of Littlewood polynomials of degree at most 12
which divide Newman polynomials. Moreover, we show that every Newman
quadrinomial $X^a+X^b+X^c+1$, $15>a>b>c>0$, has a Littlewood multiple of
smallest possible degree which can be as large as $32765$.
