In the matrix representation, the Lorentz rotor is seen to form an instance of the SL(2, C) group (special linear group of degree 2 over the complex numbers), which is the double cover of the Lorentz group. The unimodularity of the Lorentz rotor is translated in the following condition in terms of the product of the Lorentz rotor with its Clifford conjugation L L ¯ ¯ = L ¯ ¯ L = 1.