This paper discusses the splitting problem of the polynomial time bounded many one degrees. The main result is that: there exists a nonzero p-m degree a such that if a is splitted by n + 1 degrees a₀, a₁, ...,a_n for any natural number n≥1,then there exist at lesst n different pairs (a_i,a_j) (i≠j &. i,j≤n) which are not minimal paris. This generalizes Ambos-Spies' result of which asserts that there is a nonzero p-m degree which can not be splitted by any minimal pair.