We study unextendible maximally entangled bases (UMEBs) in \({{\mathbb{C}}}^{d}\otimes {{\mathbb{C}}}^{d^{\prime} }\) (d < d′). An operational method to construct UMEBs containing d(d′ − 1) maximally entangled vectors is established, 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′ − r) maximally entangled vectors in \({{\mathbb{C}}}^{d}\otimes {{\mathbb{C}}}^{d^{\prime} }\) is presented for r = 1, 2, …, d − 1. Correspondingly, two UMEBs in \({{\mathbb{C}}}^{3}\otimes {{\mathbb{C}}}^{10}\) are obtained.