In [10] it was shown that the element Sq(2n) has nilpotence height 2n2 in the mod 2 Steenrod algebra. Here the method and result are genera
lised to show that for an odd prime p the element P-p'' has nilpotence
height p(n + 1) in the mod Steenrod algebra. Some of the other result
s of [10] are also generalised to odd primes p.