  It is now well known that the K-theory of a Waldhausen category depends on
more than just its (triangulated) homotopy category (see [Schlichting]). The
purpose of this note is to show that the K-theory spectrum of a (good)
Waldhausen category is completely determined by its Dwyer-Kan simplicial
localization, without any additional structure. As the simplicial localization
is a refined version of the homotopy category which also determines the
triangulated structure, our result is a possible answer to the general
question: ``To which extent $K$-theory is not an invariant of triangulated
derived categories ?''
