From phi-mapping method we construct a fourth-order topological tensor
current in general. It is shown that the inner structure of this topo
logical tensor current, is labelled by the delta-function delta(phi),
which represents some four-dimensional singular manifolds. By investig
ating the total expansion of delta(phi), these singular manifolds carr
y the topological numbers beta(i) eta(i) naturally, which does not inv
olve any concrete models. As the generalization of Nielsen's Lagrangia
n and Nambu's action for strings, we present a new coordinate conditio
n in general relativity, which includes the Fock's coordinate conditio
n as a special case.