  We use hyperbolic functions to parametrize lepton mixing matrix using only
one input parameter $\phi$. This matrix has three mixing angles as outputs
therefore giving two predictions. In particular it predicts $U_{e3}=0$ besides
predicting correct solar and atmospheric mixing. We confine us to real $\phi$.
For complex $\phi$ mixing matrix is no longer unitary. Next we accentuate this
unitary mixing matrix with an additional small parameter $\delta$ while keeping
unitarity of the matrix exact. When this second parameter is included, with
this framework, one can handle small but non-zero $U_{e3}$. In the second case
from two input parameters one obtains three mixing angles thus one prediction.
