We define the Schur multipliers of a separable von Neumann algebra with Cartan maximal abelian self-adjoint algebra , generalizing the classical Schur multipliers of (ℓ2). We characterize these as the normal -bimodule maps on . If contains a direct summand isomorphic to the hyperfinite II1 factor, then we show that the Schur multipliers arising from the extended Haagerup tensor product ⊗eh are strictly contained in the algebra of all Schur multipliers.