Unitarity is to hermicity what orthogonality is to symmetry. (That is, conjugation by unitary matrices preserves a Hermitian matrix’s hermicity, just as conjugation by orthogonal matrices preserves a symmetric matrix’s symmetry: (OSO⁻¹)ᵀ=(OSOᵀ)ᵀ=OᵀᵀSᵀOᵀ=OSOᵀ=OSO⁻¹; (UHU⁻¹)^†=(UHU^†)^†=UH^†U^†=UHU^†=UHU⁻¹.
Source: wiktionary