Infinitesimal affine transformations of the space $(T^0_2(M_n),\nabla^H)$ over a maximally movable space $(M_n,\nabla)$ which is not projectively flat.

We consider the bundle $T^2_0M$ of tensors of type $(2,0)$ over a maximally movable affinely connected space $(M,\nabla)$. On the total space of this bundle we take the horizontal lift $\nabla^C$ of the connection $\nabla$ and construct decomposition for infinitesimal affine transformations of $\nabla^C$. Also we find the dimension of the Lie algebra of infinitesimal transformations of this space.