  Two locally generic maps f,g : M^n --> R^{2n-1} are regularly homotopic if
they lie in the same path-component of the space of locally generic maps. Our
main result is that if n is not 3 and M^n is a closed n-manifold then the
regular homotopy class of every locally generic map f : M^n --> R^{2n-1} is
completely determined by the number of its singular points provided that f is
singular (i.e., f is not an immersion).
