  In this paper we investigate the possibility to obtain locally new
Sasaki-Einstein metrics on the space $T^{1,1}$ considering a deformation of the
standard metric tensor field. We show that from the geometric point of view
this deformation leaves transverse and the leafwise metric intact, but changes
the orthogonal complement of the Reeb vector field using a particular basic
function. In particular, the family of metric obtained using this method can be
regarded as solutions of the equation associated to the Sasaki-Ricci flow on
the underlying manifold.
