The main result of this paper shows that every reciprocal Littlewood polynomial, one with {-1, 1} coefficients, of odd degree at least 7 has at least five unimodular roots, and every reciprocal Little-wood polynomial of even degree at least 14 has at least four unimodular roots, thus improving the result of Mukunda. We also give a sketch of alternative proof of the well-known theorem characterizing Pisot numbers whose minimal polynomials are in $$A_N={[{X^d+ sumlimits^{d-1}_{k=0} a_k;X^k{in} mathbb{Z}[X];:;a_k={pm}N,;0{leqslant}k{leqslant}d-1}}$$ for positive integer $N{geqslant}2$.