  For the n-dimensional integrable system with a twisted so(p,q) reduction,
Darboux transformations given by Darboux matrices of degree 2 are constructed
explicitly. These Darboux transformations are applied to the local isometric
immersion of space forms with flat normal bundle and linearly independent
curvature normals to give the explicit expression of the position vector. Some
examples are given from the trivial solutions and standard imbedding T^n\to
R^{2n}.
