A modified strongly acidic ion exchange resin of a sulfonic acid type is disclosed. Modification is conducted by ionically binding a particular N,N-di-substituted mercaptoalkylamine to a strongly acidic ion exchange resin of a sulfonic acid type. The N,N-di-substituted mercaptoalkylamine is specifically represented by the following formulae: ##STR1## wherein R.sup.1 represents hydrogen or a C.sub.1-6 alkyl group, R.sup.2 and R.sup.3 independently represent a C.sub.1-10 alkyl group, a and b denote 0-3, respectively, a+b denotes 2 or 3, and m denotes 4 or 5. The modified ion exchange resin makes an improved catalyst in the preparation of a bisphenol by the condensation reaction of a phenol with a ketone.