The irregular behavior of the hydrogen atom in the presence of strong magnetic fields is examined by means of the ionization energy and the Shannon information entropy of the excited states involved in some high-lying avoided crossings. In addition to the energy level repulsion, which is known to occur for a certain field strength in going through a chaotic region of this type, it is found that the two states: (i) show up maximal entropies for just around this critical field and (ii) exchange their informational character in that region. (C) 2003 Elsevier Science B.V. All rights reserved.