In this paper, we consider the problem of sum throughput maximization for bidirectional relay networks with block fading. Thereby, user 1 and user 2 exchange information only via a relay node, i.e., a direct link between both users is not present. We assume that channel state information at the transmitter (CSIT) is not available and/or only one coding and modulation scheme is used at the transmitters due to complexity constraints. Thus, the nodes transmit with a fixed predefined rate regardless of the channel state information (CSI). In general, the nodes in the network can assume one of three possible states in each time slot, namely the transmit, receive, and silent state. Most of the existing protocols assume a fixed schedule for the sequence of the states of the nodes. In this paper, we abandon the restriction of having a fixed and predefined schedule and propose a new protocol which, based on the CSI at the receiver (CSIR), selects the optimal states of the nodes in each time slot such that the sum throughput is maximized. To this end, the relay has to be equipped with two buffers for storage of the information received from the two users. Numerical results show that the proposed protocol significantly outperforms the existing protocols.