The stellar velocity ellipsoid of the solar neighbour (d < 200 pc) is re-examined using intermediate-old mono-abundance stellar groups with high-quality chemistry data together with parallaxes and proper motions from Gaia DR1. We find the average velocity dispersion values for the three space velocity components for the thin and thick discs of (σU, σV, σW)thin = (33 ± 4, 28 ± 2, 23 ± 2) and (σU, σV, σW)thick = (57 ± 6, 38 ± 5, 37 ± 4) km s-1, respectively. The mean values of the ratio between the semi-axes of the velocity ellipsoid for the thin disc are found to be σV/σU = 0.70 ± 0.13 and σW/σU is 0.64 ± 0.08, while for the thick disc σV/σU = 0.67 ± 0.11 and σW/σU is 0.66 ± 0.11. Inputting these dispersions into the linear Strömberg relation for the thin disc groups, we find the Sun's velocity with respect to the Local Standard of Rest in Galactic rotation to be V⊙ = 13.9 ± 3.4 km s-1. A relation is found between the vertex deviation and the chemical abundances for the thin disc, ranging from -5 to +40° as iron abundance increases. For the thick disc we find a vertex deviation of luv ∼-15°. The tilt angle (luw) in the U-W plane for the thin disc groups ranges from -10 to +15°, but there is no evident relation between luw and the mean abundances. However, we find a weak relation for luw as a function of iron abundances and α-elements for most of the groups in the thick disc, where the tilt angle decreases from -5 to -20° when [Fe/H] decreases and [α/Fe] increases. The velocity anisotropy parameter is independent of the chemical group abundances and its value is nearly constant for both discs (β ∼ 0.5), suggesting that the combined disc is dynamically relaxed. [ABSTRACT FROM AUTHOR]