  The new potential model for pionic hydrogen, constructed with the employment
of the two-body relativistic equation, is offered. The relativistic equation,
based on the extension of the $SL(2,C)$ group to the $Sp(4,C)$ one, describes
the effect of the proton spin and anomalous magnetic moment in accordance with
the results of the quantum electrodynamics. Within this approach, using the
experimental data on the strong energy level shift and width of the $1s$ state
in pionic hydrogen as input, the pion-nucleon scattering lengths have been
evaluated to be $a_{\pi^{-}p}=0.0860(6)m_{\pi}^{-1}$ and
$a_{\pi^{0}n}=-0.1223(19)m_{\pi}^{-1}$.

High Energy Physics - Phenomenology