Let KG be a group algebra of a finite p-group G over a finite field K of ch
aracteristic p. We compute the order of the unitary subgroup of the group o
f units when G is either an extraspecial a-group or the central product of
such a group with a cyclic group of order 4 or G has an abelian subgroup A
of index 2 and an element b such that b inverts each element of A.