In this paper, we present an algorithm for reducing the transmit normalization factor by perturbing the transmit signal in a Multi-User Multiple Input Multiple Output (MU-MIMO) system which uses the channel inverse matrix as its precoding matrix. A base station must normalize unnormalized transmit signals due to the limitation of the constant transmit power. This paper defines the norm of the unnormalized transmit signal as the transmit normalization factor used to normalize the transmit signal. Recalling that the transmit normalization factor consists of a combination of the singular values from the channel inverse matrix, we provide a codebook that successively reduces the coefficients of these singular values. Through computer simulations, the proposed algorithm is compared to sphere encoding in terms of the Bit Error Rate (BER) and the outage probability in a MU-MIMO signal environment. Sphere encoding is known to be an optimal solution amongst the perturbation methods that reduce the transmit normalization factor [1]. This work demonstrates that the proposed algorithm is has very good performance, comparable to that of sphere encoding, while its computational load is nearly 200 times less. Since the codebook in our algorithm depends only on the given channel, the difference in the computational complexity becomes even greater when the channel state is not changed, because the codebook can be reused. Furthermore, the codebook exhibits the characteristic of robustness to the maximum Doppler shift.