  Let $m$ be a square-free positive integer, $m\equiv 2,3 \; (\bmod \; 4)$. We
show that the number field $K=Q(i,\sqrt[4]{m})$ is non-monogene, that is it
does not admit any power integral bases of type $\{1,\alpha,\ldots,\alpha^7\}$.
In this infinite parametric family of Galois octic fields we construct an
integral basis and show non-monogenity using only congruence considerations.
  Our method yields a new approach to consider monogenity or to prove
non-monogenity in algebraic number fields. It is well applicable in parametric
families of number fields. We calculate the index of elements as polynomials
depending on the parameter, factor these polynomials and consider systems of
congruences according to the factors.
