  We analyze statistical properties of the complex system with conditions which
manifests through specific constraints on the column/row sum of the matrix
elements. The presence of additional constraints besides symmetry leads to new
correlations among eigenfunctions, hinders their complete delocalization and
affects the eigenvalues too. Our results reveal a rich behavior hidden beneath
the spectral statistics and also indicate the presence of a new universality
class analogous to that of a Brownian ensemble appearing between Poisson and
Gaussian orthogonal ensemble.
