Pseudo random binary sequences have been widely used in cryptographic applications due to their speedy construction, reproducibility and characteristics like true random sequence. Realization of modern cryptographic application and mathematical tools is inconceivable without random sequences. Previously, we proposed an alternative trace map function for generation of a pseudo random binary sequence that has long period, good correlation characteristics and high linear complexity that are attractive for security applications. However, it was found that the distribution of bits in sequence is not uniform which may lead to failure in randomness. In this paper, we propose a uniformization method using power of primitive root to improve uniformity of bit distribution in the sequence. Sequence of different lengths is generated using proposed sequence to verify the efficiency of the proposed uniformization method. By analyzing the bit distribution of generated sequences for different length of patterns, we show that the proposal achieves bit uniformity while maintaining randomness of the sequence.