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Abstract. A theorem of F. Hirzebruch relates continued fractions to class numbers of quadratic number fields. A version for function fields of odd characteristic was established by D. R. Hayes and C. D. González. We present here a complete treatment of the even charateristic theory, in particular, two class number relations involving continued fractions are derived, one of which is an analogue of the Hirzebruch relation in characteristic 2. The following result of F. Hirzebruch ([5], cf. also [8]) relates continued fraction to class number of quadratic number fields. Theorem. (Hirzebruch) Let p be a prime with p ≡ 3 (mod 4) and p> 3