We give examples of subcanonical subvarieties of codimen-sion 3 in projective ra-space which are not Pfaffian, i.e. defined by the ideal sheaf of submaximal Pfaffians of an alternating map of vector bun-dles. This gives a negative answer to a question asked by Okonek [29]. Walter [36] had previously shown that a very large majority of sub-canonical subschemes of codimension 3 in Pnare Pfaffian, but he left open the question whether the exceptional non-Pfaffian cases actually occur. We give non-Pfaffian examples of the principal types allowed by his theorem, including (Enriques) surfaces in P5in characteristic 2 and a smooth 4-fold in. These examples are based on our previous work [14] showing that any strongly subcanonical subscheme of codimension 3 of a Noetherian scheme can be realize as a locus of degenerate intersection of a pair of Langrangian (maximal isotropic)subbundles of a twisted orthogonal bundle