A parametrisation of the degenerate neutrino mass matrix obeying $mu -tau$ symmetry, is introduced for detailed numerical analysis. As a continuation of our earlier work on normal and inverted hierarchical models, the present parametrisation for degenerate models has the ability to lower the solar mixing angle below the tri-bimaximal value $tan^{2}theta_{12}=0.5$, while maintaining the condition of maximal atmospheric mixing angle and zero reactor angle. The combined data on the mass-squared differences derived from various oscillation experiments, and also from the bounds on absolute neutrino masses in $0 ubetabeta$ decay and cosmology, gives certain constraints on the validity of the degenerate models.
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