Mutually Unbiased Unextendible Maximallyentangled Bases In C2 ⊗C3

Firstly, this paper uses the Gell-Mann matrices to construct 4-member unextendible maximally entangled basis in  C2⊗C3 , whose construction is different from those in literatures, then adds two product states to make it complete. Finally, by changing the basis of  C3, this paper constructs a pair of mutually unbiased unextendible maximally entangled bases C2⊗C3.