  Hamiltonian and eigenstate problem is formulated for a bilayer graphene in
terms of Clifford's geometric algebra \textit{Cl}$_{3,1}$. It is shown that
such approach allows to perform analytical calculations in a simple way if
geometrical algebra rotors are used. The measured quantities are express
through spectrum and rotation half-angle of the pseudospin that appears in
geometric algebra rotors. Properties of free charge carriers -- pseudospin,
velocity and Berry phase -- in a bilayer graphene are investigated in the
presence of the external voltage applied between the two layers.
