This paper presents an improved technique for guaranteed zonotopic state estimation of Multi-Output discrete-time linear-time invariant systems subject to unknown but bounded disturbances and measurement noises, in the presence of interval uncertainties. The estimation procedure is based on the minimization of the P-radius of the zonotopic state estimation domain, which guarantees the non-increasing property of the guaranteed zonotopic state estimation at each time instant. This paper proposes an original result on the zonotopic approximation of the intersection between a zonotope (state prediction domain) and a polytope (obtained when considering the measurements of all the system outputs at the same time).