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We solved the unextendible maximally entangled basis (UMEB) problem in$\mathbb{C}^{d}\bigotimes\mathbb{C}^{d'}(d\neq d')$,the results turn out to bethat there always exist a UMEB.In addition,there might be two sets of UMEB withdifferent numbers.The main difficult is to prove the unextendibility of the setof states.We give an explicit construction of UMEB by considering the Schmidtnumber of the complementary space of the states we construct.

Unextendible maximally entangled bases in $\mathbb{C}^{d}\bigotimes\mathbb{C}^{d'}$