We give a small, but very useful modification of a criterion of Mignotte ([4]) for Catalan’s equation, replacing the class number of a certain abelian field by the relative class number, which is much easier to compute. The proof is the same, apart from the idea to consider the class group modulo the ideals coming from the real subfield. We use the following notation: K is a CM-field, IK its group of fractional ideals and i : K∗ → IK the canonical map x 7→ (x); j denotes complex conjugation, K+ the maximal real subfield and h−(K) the relative class number of K; OK is the ring of integral elements of K. Lemma 1. Let K be a CM-field and Q a finite set of prime ideals of K. There is a subgroup I0 of the ideal group IK such that (i) the prime ideals in Q do not appear in the factorization of any ideal in I0; (ii) IK/(i(K∗)I0) has cardinality h−(K) or 2h−(K); (iii) if e ∈ K∗ with (e) ∈ I0, then e1−j is a root of unity. P r o o f. Let I0 consist of those ideals which are in the image of the canonical map IK+ → IK , and which do not contain any prime ideal in Q. If (e) ∈ I0, then (e) = (e), so e1−j is a unit, hence also a root of unity because all its conjugates have absolute value 1 (cf. [6], Lemma 1.6). It remains to show (ii). It is an easy consequence of the approximation theorem that every ideal class contains an ideal without primes in Q (see e.g. [3], IV, Corollary 1.4). Therefore IK/(i(K∗)I0) = ideal class group of K modulo image of the ideal class group of K+. By [6], Theorem 10.3, at most 2 ideal classes of K+ become principal in K, so the statement follows. Theorem 1. Let p 6= q be odd prime numbers. Let ζ be a primitive p-th root of unity and K an imaginary subfield of L := Q(ζ). Catalan’s equation x − y = 1 has no nontrivial integral solution if q -h−(K) and pq−1 6≡ 1 mod q2.