  We introduce a canonical form for reduced bases of integral closures of
discrete valuation rings, and we describe an algorithm for computing a basis in
reduced normal form. This normal form has the same applications as the Hermite
normal form: identification of isomorphic objects, construction of global bases
by patching local ones, etc. but in addition the bases are reduced, which is a
crutial property for several important applications. Except for very particular
cases, a basis in Hermite normal form cannot be reduced.
