Available online xxxx Communicated by Louis Rowen MSC: 16W10 16W25 16K20 11E39 Keywords: Central simple algebra Involution Quaternion algebra Frobenius algebra Bilinear and quadratic form Pfister formA necessary and sufficient condition for a central simple algebra with involution over a field of characteristic two to be decomposable as a tensor product of quaternion algebras with involution, in terms of its Frobenius subalgebras, is given. It is also proved that a bilinear Pfister form, recently introduced by A. Dolphin, can classify totally decomposable central simple algebras of orthogonal type.