In this paper, we study a class of Finsler metrics, which are defined by a Riemannian metric α and a one-form β. They are called general (α, β)-metrics. We have proven that, every Landsberg general (α, β)-metric is a Berwald metric, under a certain condition. This shows that the hunting for an unicorn, one of the longest standing open problem in Finsler geometry, cannot be successful in the class of general (α, β)-metrics.