Chemical bonding in MgO and TiO₂ crystals is analyzed using a minimal basis consisting of atomic-type Wannier functions (AWFs) centered at atomic sites in the crystal and constructed from Bloch states of the energy bands originating from the valence states of the atoms. A method proposed earlier for constructing Wannier functions is improved. Symmetrization of the initial Bloch function basis and symmetrical orthogonalization of the generalized Bloch functions greatly reduces computational effort. The prior symmetrization of the Bloch function basis is of fundamental importance in constructing AWFs, because the latter functions have to be centered at the atomic sites and possess the symmetry of the atomic functions in the crystal. The principle that should be followed in selecting the conduction bands originating from the valence states of the atoms of the crystal is formulated. The Bloch functions are calculated using the LCAO approximation within the Hartree-Fock method and density-functional theory. Using the calculated Bloch functions, a minimal valence AWF basis is constructed and calculations of the local characteristics of the electronic structure (atomic charge, bond order, atomic valence) are performed for the MgO and TiO₂ crystals. According to the analysis performed, the covalent component of the chemical bonding in the MgO crystal is negligibly small and TiO₂ is a mixed ionic and covalent crystal with pronounced covalent bonding.