Recently, a fully supervised speaker diarization approach was proposed (UIS-RNN) which models speakers using multiple instances of a parameter-sharing recurrent neural network. In this paper we propose qualitative modifications to the model that significantly improve the learning efficiency and the overall diarization performance. In particular, we introduce a novel loss function, we called Sample Mean Loss and we present a better modelling of the speaker turn behaviour, by devising an analytical expression to compute the probability of a new speaker joining the conversation. In addition, we demonstrate that our model can be trained on fixed-length speech segments, removing the need for speaker change information in inference. Using x-vectors as input features, we evaluate our proposed approach on the multi-domain dataset employed in the DIHARD II challenge: our online method improves with respect to the original UIS-RNN and achieves similar performance to an offline agglomerative clustering baseline using PLDA scoring.