La(3.2)Ba(0.8)Mn(3)O(10), a representative of the rare n = 3 members of the Ruddlesden-Popper manganites A(n+1)Mn(n)O(3n+1), was synthesized in an evacuated sealed silica tube. Its crystal structure was refined from a combination of powder X-ray diffraction (PXD) and precession electron diffraction (PED) data, with the rotations of the MnO(6) octahedra described within the symmetry-adapted mode approach (space group Cccm, a = 29.068(1) Å, b = 5.5504(5) Å, c = 5.5412(5) Å; PXD R(F) = 0.053, R(P) = 0.026; PED R(F) = 0.248). The perovskite block in La(3.2)Ba(0.8)Mn(3)O(10) features an octahedral tilting distortion with out-of-phase rotations of the MnO(6) octahedra according to the (Φ,Φ,0)(Φ,Φ,0) mode, observed for the first time in the n = 3 Ruddlesden-Popper structures. The MnO(6) octahedra demonstrate a noticeable deformation with the elongation of two apical Mn-O bonds due to the Jahn-Teller effect in the Mn(3+) cations. The relationships between the octahedral tilting distortion, the ionic radii of the cations at the A- and B-positions, and the mismatch between the perovskite and rock-salt blocks of the Ruddlesden-Popper structure are discussed. At low temperatures, La(3.2)Ba(0.8)Mn(3)O(10) reveals a sizable remnant magnetization of about 1.3 μ(B)/Mn at 2 K, and shows signatures of spin freezing below 150 K.