I have a question about subbundles of tangent bundles. If i have a subbundle E of TM and a local frame X_1,..,X_n of TM ,s.t. X_1,..,X_{n-q} is a local frame of E.

Is it right, that the dual frame w_1,...,w_n of TM* has the property that w_1,....,w_{n-q} forms a frame for E*?

Thank you.