  The Bethe-Salpeter amplitude $\Phi(k,p)$ is expressed, by means of the
Nakanishi integral representation, via a smooth function $g(\gamma,z)$. This
function satisfies a canonical equation $g=Ng$. However, calculations of the
kernel $N$ in this equation, presented previously, were restricted to one-boson
exchange and, depending on method, dealt with complex multivalued functions.
Although these difficulties are surmountable, but in practice, they complicate
finding the unambiguous result.
  In the present work, an unambiguous expression for the kernel $N$ in terms of
real functions is derived. For the one-boson scalar exchange, the explicit
formula for $N$ is found. With this equation and kernel, the binding energies,
calculated previously, are reproduced. Their finding, as well as calculation of
the Bethe-Salpeter amplitude in the Minkowski space, become not more difficult
than in the Euclidean one. The method can be generalized to any kernel given by
irreducible Feynman graph. This generalization is illustrated by example of the
cross-ladder kernel.
