  For any quartic number field $K$ generated by a root $\alpha$ of an
irreducible trinomial of type $x^4+ax^2+b\in Z[x]$, we characterize when
$Z[\alpha]$ is integrally closed. Also for $p=2,3$, we explicitly give the
highest power of $p$ dividing $i(K)$, the common index divisor of $K$. For a
wide class of monogenic trinomials of this type we prove that up to equivalence
there is only one generator of power integral bases in $K=Q(\alpha)$. We
illustrate our statements with a series of examples.
