Kikianty and Dragomir in 2008 introduced the p-HH-norms on
the Cartesian product of two copies of a normed space, which are equivalent
to the well-known p-norms. In this paper, notions of orthogonality in terms of
2-HH-norms are introduced. The main properties of these orthogonalities are
discussed. Several characterizations of inner product spaces are established,
as well as the characterization of strictly convex spaces.