We study the unextendible entangled bases with fixed Schmidt number (UEBk) in $$\mathbb {C}^d\otimes \mathbb {C}^{d'}$$ Cd⊗Cd′ which play a significant role in quantum information processing. We first give the construction of the UEBk when $$d'$$ d′ is not the multiple of k and illustrate two different UEBks in $$\mathbb {C}^3\otimes \mathbb {C}^7$$ C3⊗C7 and $$\mathbb {C}^4\otimes \mathbb {C}^{10}$$ C4⊗C10 . Then, we present the construction of the UEBk when $$d'$$ d′ is the multiple of k and illustrate them in $$\mathbb {C}^7\otimes \mathbb {C}^8$$ C7⊗C8 , $$\mathbb {C}^4\otimes \mathbb {C}^9$$ C4⊗C9 , $$\mathbb {C}^8\otimes \mathbb {C}^8$$ C8⊗C8 and $$\mathbb {C}^4\otimes \mathbb {C}^8$$ C4⊗C8 . Our constructions of UEBk generalize the results in Guo [Phys Rev A 90 : 054303, 2014].