Revenel computed the Adams spectral sequence converging to BP(Ω$^2$S(sup)2n+1) and got the E(sub)$infty$-term. Then he gave the conjecture about the extension. Here we prove that there should be non-trivial extension. We also study the BP(sub)*BP comodule structures on the polynomial algebras which are related with BP(sub)*(Ω$^2$S(sup)2n+1).