The product of two Lorentz boosts in different directions is equal to the product of a pure boost and a spatial rotation. To second order, the resulting boost is simply the sum of the individual boosts, and the rotation is responsible for the Thomas precession. Here the resulting boost and the rotation correction are calculated exactly. The calculation of higher‐order corrections to the sum of two finite Lorentz boosts is not usually done, and here previous exact results are critically compared. The complete expression is, to the best of the author’s knowledge, a new result.