Let X be an irreducible holomorphic symplectic manifold of K3 [n] deformation type, n ≥ 2. There exists over X ×X a rank 2n−2 rigid and stable reflexive sheaf A of Azumaya algebras, constructed in [Ma5], such that the pair (X × X, A) is deformation equivalent to the following pair (M × M, AM ). The manifold M is a smooth and compact moduli space of stable sheaves over a K3 surface S, and AM is the reflexive sheaf, whose fiber, over a pair (F1, F2) ∈ M × M of non-isomorphic stable sheaves F1 and F2, is End Ext 1 S (F1, F2) . We prove in this paper the following uniqueness result.Let A1 and A2 be two rigid Azumaya algebras over X × X, which are (ω, ω)-slope-stable with respect to the same Kähler class ω on X, and such that (X × X, Ai) is deformation equivalent to (M × M, AM ), for i = 1, 2. Assume that the singularities of A1 and A2 along the diagonal are of the same infinitesimal type prescribed by AM . Then A1 is isomorphic to A2 or A * 2 . Furthermore, if P ic(X) is trivial, or cyclic generated by a class of non-negative Beauville-Bogomolov-Fujiki degree, then there exists a unique pair {A, A * }, such that (X × X, A) is deformation equivalent to (M × M, AM ), and A is (ω, ω)-slope-stable with respect to every Kähler class ω on X.The above is the main example of a more general global Torelli theorem proven. The result is used in the authors forthcoming work on generalized deformations of K3 surfaces. EYAL MARKMAN AND SUKHENDU MEHROTRA 4.2. Local moduli space of reflexive Azumaya algebras 31 4.3. A global moduli space 34 5. Stability and separability 35 6. A global Torelli theorem 36 7. Proof of Theorem 1.11 establishing the main example 38 References 43From now on the term a sheaf of Azumaya algebras will mean a reflexive sheaf of Azumaya O X -algebras. A subsheaf P of a sheaf E of Azumaya algebras is a sheaf of maximal parabolic subalgebras if, in the notation of Definition 1.1, η α (P | Uα ) is the sheaf of subalgebras of End(F α )1 Caution: The standard definition of a sheaf of Azumaya OX -algebras assumes that E is a locally free OXmodule, while we assume only that it is reflexive.