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We study unextendible maximally entangled bases (UMEBs) in $\mathbb{C}^{d}\otimes \mathbb {C}^{d^{\prime}}$ ($d<d'$). An operational method toconstruct UMEBs containing $d(d^{\prime}-1)$ maximally entangled vectors isestablished, and two UMEBs in $\mathbb {C}^{5}\otimes \mathbb {C}^{6}$ and$\mathbb {C}^{5}\otimes \mathbb {C}^{12}$ are given as examples. Furthermore,a systematic way of constructing UMEBs containing $d(d^{\prime}-r)$ maximallyentangled vectors in $\mathbb {C}^{d}\otimes \mathbb {C}^{d^{\prime}}$ ispresented for $r=1,2,\cdots, d-1$. Correspondingly, two UMEBs in $\mathbb{C}^{3}\otimes \mathbb {C}^{10}$ are obtained.

Constructions of Unextendible Maximally Entangled Bases in \(\mathbb {C}^{d}\otimes \mathbb {C}^{d^{\prime}}\)