A basic fact taught in undergraduate algebra courses is that every finite nilpotent group is a direct product of p-groups. Already Bruck [5] observed that this does not generalize to loops. In particular, there exist nilpotent loops of size 6 which are not direct products of loops of size 2 and 3. Still we show that every finite nilpotent loop \((A,\cdot )\) has a binary term operation \(*\) such that \((A,*)\) is a direct product of nilpotent loops of prime power order, i.e., \((A,*)\) is supernilpotent. As an application we obtain that every nilpotent loop of order pq for primes p, q has a finite basis for its equational theory.
