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We determine the bounday of the fully polarized ferromagnetic states in the one dimensional Kondo lattice model at partial conduction electron band filling by using a newly developed infinite size DMRG method which conserves the total spin quantum numbers. The obtained paramagnetic to ferromagnetic phase bounday is bellow J ≍ 3.5 for the whole range of band filling. By this we solve the controversy in the phase diagram over the extent of the ferromagnetic region close to half filling.