It is well kowned that C-reducible Finsler space must to be L-reducible Finsler space, but the opposite is not true. This paper studies the conditions for the opposite turning to be true. It contains that under three different conditions, the L-reducible Finsler space can turn to be C-reducible Finsler space. First, considering that Finsler space with isotropic Landsberg curvature is related with Cartan torsion and Landsberg curvature，so it may turn to be related with mean Cartan torsion and mean Landsberg curvature, it gets Theorem 1: If the L-reducible Finsler space is with isotropic Landsberg curvature, it must turn to be C-reducible Finsler space. Then, the author studies L-reducible Finsler space with constant curvature, and proves that it can turn to be C-reducible Finsler space too. Under such two cases, through comparing the relation between the Landsberg curvature and the Cartan torsion, this paper gets a sepecial corollary: If the L-reducible Finsler space satisefies , where , it must be C-reducible Finsler space. At last, being inspired by Theorem 2 , the author considers the relation between constant cuvature and scalar cuvature, and finds that L-reducible Finsler space with scalar cuvature is also C-reducible Finsler space，and gets the form of the mean Cartan torsion