We study maximally entangled bases in bipartite systems $\mathbb {C}^d ⊗ \mathbb {C}^{kd}\ (k𝟄 Z^{+})$ Cd⊗Ckd(k∈Z+) , which are mutually unbiased. By systematically constructing maximally entangled bases, we present an approach in constructing mutually unbiased maximally entangled bases. In particular, five maximally entangled bases in $\mathbb {C}^2 ⊗ \mathbb {C}^{4}$ C2⊗C4 and three maximally entangled bases in $\mathbb {C}^2 ⊗ \mathbb {C}^{6}$ C2⊗C6 that are mutually unbiased are presented.