Let D be a division ring with an involution - and F = {a ∈ D | ̄a = a}. When - is the identity map then D = F is a field and we assume char(F) ≠ 2. When - is not the identity map we assume that F is a subfield of D and is contained in the center of D. Let n be an integer, n ≥ 2, and ℋn(D) be the space of hermitian matrices which includes the space Sn(F) of symmetric matrices as a particular case. If a bijective map φ of ℋn(D) preserves the adjacency then also φ-1 preserves the adjacency.