Summary: We prove that two 2-blocks of (possibly different) finite groups with a common minimal nonabelian defect group and the same fusion system are isotypic (and therefore perfectly isometric) in the sense of Broué. This continues former work by M. Cabanes and C. Picaronny [J. Fac. Sci., Univ. Tokyo, Sect. I A 39, No. 1, 141–161 (1992; Zbl 0781.20006)], the author [J. Algebra 337, No. 1, 261–284 (2011; Zbl 1247.20010)] and C. W. Eaton et al. [J. Group Theory 15, No. 3, 311–321 (2012; Zbl 1253.20008)].