We study the global topological structure of hypersurfaces in ℂP ⁿ⁺¹, n ≥ 3, with quadratic singularities and prescribed set of singular points. Under certain restrictions on the degree, we give a precise topological description of such a hypersurface by decomposing it into a connected sum of special form. In this case, the diffeomorphism type of the hypersurface is determined by the dimension, degree, and the number of singular points.