The IEEE 802.11ah standard relies on the conventional distributed coordination function (DCF) as a backoff selection method. The DCF is utilized in the contention-based period of the newly introduced medium access control (MAC) mechanism, namely restricted access window (RAW). Despite various advantages of RAW, DCF still utilizes the legacy binary exponential backoff (BEB) algorithm, which suffers from a crucial disadvantage of being prone to high probability of collisions with high number of contending stations. To mitigate this issue, this paper investigates the possibility of replacing the existing exponential sequence (i.e., as in BEB) with a better pseudorandom sequence of integers. In particular, a new backoff algorithm, namely Pseudorandom Sequence Contention Algorithm (PRSCA) is proposed to update the CW size and minimize the collision probability. In addition, the proposed PRSCA incorporates a different approach of CW freezing mechanism and backoff stage reset process. An analytical model is derived for the proposed PRSCA and presented through a discrete 2-D Markov chain model. Performance evaluation demonstrates the efficiency of the proposed PRSCA in reducing collision probability and improving saturation throughput, network throughput, and access delay performance.