A modification of the original definition of Stiefel-Whitney classes $w_{i}$ is given. A geometrical specification of the construction of Teleman's classes $t_{i}$, defined in [5], is also given. A direct proof of the equalities $t_{i}(\xi) = w_{i}(\eta)$ follows, when $\eta$, $\xi$ are a real vector bundle and the associated sphere bundle with antipodal involution.