Summary: The authors examine the properties of the quantum Lorentz group \(SO_ q(3,1)\) using the \(R\)-matrix given in their paper [Z. Phys. C 48, 159-165 (1990)]. They show that this matrix together with the \(q\)-deformed metric \(C\) provide a representation of a BWM (Birman-Wenzl-Murakami) algebra. Using the projection operators which decompose the \(R\) matrix into irreducible components, we give the general definition of the corresponding quantum space, i.e. the \(q\)-deformed Minkowski space and the \(q\)-deformed Clifford algebra. We also construct the \(q\) analog of Dirac matrices and show that they form a matrix representation of the \(q\)-deformed Clifford algebra.