Let n≥5. There is a smoothly knotted n-dimensional sphere in (n+2)-space such that the singular point set of its projection in (n+1)-space consists of double points and that the components of the singular point set are two. (The sphere is knotted in the sense that it does not bound any embedded (n+1)-ball in (n+2)-space.) Furthermore, the projection is not the projection of any unknotted sphere in (n+2)-space. There are two inequivalent embeddings of an n-manifold in (n+2)-space such that the singular point set of the projection of each embedding consists of double points and that the number of components of the singular point set of each embedding is one.