Owing to most physical phenomena observed as nonstationary processes and the form of discrete sequences, it becomes realistic to process the nonstationary sequences in the laboratory if there exists a bi jective transformation for stationarization. In this work, our study is emphasized on the class of nonstationary one-dimensional random sequences with wide-sense stationary increments (WSSI), wide-sense stationary jumps (WSSJ) and a famous case, the fractional Brownian motion (FBM) process. Also, the concept of linear algebra is applied to process the stationarization concisely. Our goal is to derive a stationarization theorem developed by linear operators such that a nonstationary sequence with WSSI/WSSJ may be stationarized by an easily realizable perfect reconstruction-quadrature mirror filter structure of the discrete wavelet transform. Some examples for FBM processes and nonstationary signals generated by autoregressive integrated moving average models are provided to demonstrate the stationarization.