Low latency is one of the desired properties for partially synchronous Byzantine consensus protocols. Previous protocols have achieved consensus with just two communication steps either by reducing the bound on the number of faults the protocol can tolerate ($f \leq \frac{n-1}{5}$) or use of trusted hardware like Trusted Execution Environment or TEEs. In this paper, we propose a protocol called Fast B4B, in which the protocol achieves consensus in just two communication steps. Fast B4B can tolerate maximum number of faults a partial BFT consensus can tolerate ($f \leq \frac{n-1}{3}$). Furthermore, Fast B4B does not require the use of any trusted hardware. The trade-off for this achievement is that at most $f$ times some nodes may revert their blocks. We show that this reversion of a block will not compromise the safety of the protocol at all, yet it may incur a small amount of additional latency during view change.