  We calculate the energy level displacement of the excited $np$ state of
kaonic deuterium in terms of the P-wave scattering length of $K^-d$ scattering.
We solve the Faddeev equations for the amplitude of $K^-d$ scattering in the
fixed centre approximation and derive the complex P-wave scattering length of
$K^-d$ scattering in terms of the S-wave and P-wave scattering lengths of
$\bar{K}N$ scattering. The estimated uncertainty of the complex P-wave
scattering length is of about $15\,%$. For the calculated width $\Gamma_{2p} =
10.203\,{\rm meV}$ of the excited $2p$ state of kaonic deuterium we evaluate
the yield $Y_{K^-d} = 0.27\,%$ of $X$-rays for the $K_{\alpha}$ emission line
of kaonic deuterium. Using the complex S-wave and P-wave scattering lengths of
$\bar{K}N$ scattering, calculated in \cite{ECL1,Weise1}, we get the width
$\Gamma_{2p} = 2.675\,{\rm meV}$ of the excited $2p$ state and the yield
$Y_{K^-d} = 1.90 \,%$ of $X$-rays for the $K_{\alpha}$ emission line of kaonic
deuterium. The results, obtained in this paper, can be used for the planning of
experiments on the measurements of the energy level displacement of the ground
state of kaonic deuterium, caused by strong low-energy interactions.

Nuclear Theory