Abstract: The theorems of Altman-type fixed point are studied. The existence of the fixed point of completely continuous operator is discussed under the norm inequality conditions that the first exponent is between 0 and 1, the second one is not greater than 0 and there is only one exponent that is less than 0. Some new fixed point theorems are proved. In contrast to the fixed point theorems as shown in earlier works where the first exponent is greater than 1 and the second one is not less than 0 under the norm inequality conditions, some supplements are given to those theorems.