Recent diarization technologies can be categorized into two approaches, i.e., clustering and end-to-end neural approaches, which have different pros and cons. The clustering-based approaches assign speaker labels to speech regions by clustering speaker embeddings such as x-vectors. While it can be seen as a current state-of-the-art approach that works for various challenging data with reasonable robustness and accuracy, it has a critical disadvantage that it cannot handle overlapped speech that is inevitable in natural conversational data. In contrast, the end-to-end neural diarization (EEND), which directly predicts diarization labels using a neural network, was devised to handle the overlapped speech. While the EEND, which can easily incorporate emerging deep-learning technologies, has started outperforming the x-vector clustering approach in some realistic database, it is difficult to make it work for `long' recordings (e.g., recordings longer than 10 minutes) because of, e.g., its huge memory consumption. Block-wise independent processing is also difficult because it poses an inter-block label permutation problem, i.e., an ambiguity of the speaker label assignments between blocks. In this paper, we propose a simple but effective hybrid diarization framework that works with overlapped speech and for long recordings containing an arbitrary number of speakers. It modifies the conventional EEND framework to simultaneously output global speaker embeddings so that speaker clustering can be performed across blocks to solve the permutation problem. With experiments based on simulated noisy reverberant 2-speaker meeting-like data, we show that the proposed framework works significantly better than the original EEND especially when the input data is long.