Let T = T (n1,n2, · · · ,nk ) ⊆ Mn(C ) be a block upper triangular matrix algebra and let M be a 2-torsion free unital T -bimodule, where C is a commutative ring. Let Δ :T →M be a C -linear map. We show that if Δ(X)Y +XΔ(Y)+Δ(Y)X +YΔ(X)=0 whenever X,Y ∈ T are such that XY = YX = 0, then Δ(X) = D(X)+α(X)+XΔ(I), where D : T → M is a derivation, α : T →M is an antiderivation, I is the identity matrix and Δ(I)X = XΔ(I) for all X ∈ T . We also prove that under some sufficient conditions on T , we have α = 0. As a corollary, we show that under given sufficient conditions, each Jordan derivation Δ : T →M is a derivation and this is an answer to the question raised in [9]. Some previous results are also generalized by our conclusions.
