  The decomposition of a two dimensional complex germ with non-isolated
singularity into semi-algebraic sets is given. This decomposition consists of
four classes: Riemannian cones defined over a Seifert fibered manifold, a
topological cone over thickened tori endowed with Cheeger-Nagase metric, a
topological cone over mapping torus endowed with Hsiang-Pati metric and a
topological cone over the tubular neighbourhoods of the link's singularities.
In this decomposition there exist semi-algebraic sets that are metrically
conical over the manifolds constituting the link. The germ is reconstituted up
to bi-Lipschitz equivalence to a model describing its geometric behavior.
