In this work, we present a novel inner product design for stochastic computing. Stochastic computing is an emerging computing technique, that encodes a number in the probability of observing a one in a random bit stream. This leads to reduced hardware costs and high error tolerance. The proposed inner product design is based on a two-line bipolar encoding format and applies sequential processing of the input in a central accumulation unit. Sequential processing significantly increases the computation accuracy, since it allows for preliminary cancelation of carry bits. Moreover, the central accumulation unit gives a much better scalability compared to conventional adder tree approaches. We show that the proposed inner product design outperforms state-of-the-art designs in terms of hardware costs for high accuracy requirements and fault tolerance.