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Entanglement distillation is a key task in quantum-information processing. Inthis paper, we distill non-positive-partial-transpose (NPT) bipartite states ofsome given Schmidt rank and matrix rank. We show that all bipartite states ofSchmidt rank two are locally equivalent to classical-classical states, and allbipartite states of Schmidt rank three are 1-undistillable. Subsequently, weshow that low-rank B-irreducible NPT states are distillable for large-rankreduced density operators by proving low-rank B-irreducible NPT state whoserange contains a product vector is distillable. Eventually, we present anequivalent condition to distill $M\times N$ bipartite states of rank$\max\{M,N\}+1$.

Entanglement distillation in terms of Schmidt rank and matrix rank