  It is known that sometimes a Belyi pair is not defined over its field of
moduli. Instead, it is defined over a finite degree extension of its field of
moduli, called a field of definition. We show that given a number $m$ there
exists a Belyi pair such that the degree of a field of definition over the
field of moduli is greater than $m$. As a byproduct, we obtain a counterexample
to the local-global principle for Belyi pairs.
