  An orthogonality relation for the Whittaker functions of the second kind of
imaginary order, $W_{\kappa,\mathrm{i}\mu}(x)$, with $\mu\in\mathbb{R}$, is
investigated. The integral $\int_{0}^{\infty}\mathrm{d}x\:
x^{-2}W_{\kappa,\mathrm{i}\mu}(x)W_{\kappa,\mathrm{i}\mu'}(x)$ is shown to be
proportional to the sum $\delta(\mu-\mu')+\delta(\mu+\mu')$, where
$\delta(\mu\pm\mu')$ is the Dirac delta distribution. The proportionality
factor is found to be
$\pi^{2}/[\mu\sinh(2\pi\mu)\Gamma({1/2}-\kappa+\mathrm{i}\mu)
\Gamma({1/2}-\kappa-\mathrm{i}\mu)]$. For $\kappa=0$ the derived formula
reduces to the orthogonality relation for the Macdonald functions of imaginary
order, discussed recently in the literature.
