  In the paper, we show that when a quantum state can be decomposed as a convex
combination of locally orthogonal mixed states, its entanglement can be
decomposed into the entanglement of these mixed states without losing them. The
obtained result generalizes a corresponding one proved by Horodecki [Acta Phys.
Slov. 48, 141 (1998).]. But, for the entanglement cost it requires certain
conditions for holding the decomposition, and the distillable entanglement only
has a week result as inequality. Finally, we presented an example to show that
the conditions of our conclusions are existence.
