  Spherically symmetric solutions admitting a homothetic Killing vector field
(HKVF) either orthogonal, $\eta_{\bot}$, or parallel,$\eta_{||}$, to the
4-velocity vector field, $u^a$, are studied. New self-similar solution of
Einstein's field equation is found in the case when HKVF is in a general form.
Some physical properties of the obtained solution are examined.
