  In characteristic two, it is shown that a central simple algebra of degree
equal to a power of two with anisotropic orthogonal involution is totally
decomposable, if it becomes either anisotropic or metabolic over all extensions
of the ground field. A similar result is obtained for the case where this
algebra with involution is Brauer-equivalent to a quaternion algebra and it
becomes adjoint to a bilinear Pfister form over all splitting fields of the
algebra.
