  We associate to every central simple algebra with involution of orthogonal
type in characteristic two a totally singular quadratic form which reflects
certain anisotropy properties of the involution. It is shown that this
quadratic form can be used to classify totally decomposable algebras with
orthogonal involution. Also, using this form, a criterion is obtained for an
orthogonal involution on a split algebra to be conjugated to the transpose
involution.
