Abstract
We prove that a number field $K$ satisfies the following property (B) if and only if the ray class group of $K$ defined modulo 4 is trivial. (B): For any tame abelian extensions $N_1$ and $N_2$ over $K$ of exponent 2, the composite $N_1N_2/K$ has a relative normal integral basis (NIB) if both $N_1/K$ and $N_2/K$ have a NIB.
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