  This paper, we define the Mus-Gradient metric on tangent bundle $TM$ by a
deformation non-conform of Sasaki metric over an n-dimensional Riemannian
manifold $(M, g)$. First we investigate the geometry of the Mus-Gradient metric
and we characterize a new class of proper biharmonic maps. Examples of proper
biharmonic maps are constructed when all of the factors are Euclidean spaces.
