Let X be an H-locally convex space, i.e. a locally convex vector space the topology of which is generated by a system of separating Hilbertian seminorms \(P=\{p_{\alpha}:\alpha \in A\}\), denote the semi-inner products by \((.,.)_{\alpha}\), \(\alpha\in A\). In this paper the concept of orthogonality with respect to all semi-inner products \((.,.)_{\alpha}\) is studied. With the help of this concept some sufficient conditions of normability of H-locally convex spaces are obtained. Finally the notion of an adjoint operator, again with respect to all semi-inner products in an H-locally convex space is treated, which gives another sufficient condition for normability.