This paper presents a new deep clustering (DC) method called manifold-aware DC (M-DC) that can enhance hyperspace utilization more effectively than the original DC. The original DC has a limitation in that a pair of two speakers has to be embedded having an orthogonal relationship due to its use of the one-hot vector-based loss function, while our method derives a unique loss function aimed at maximizing the target angle in the hyperspace based on the nature of a regular simplex. Our proposed loss imposes a higher penalty than the original DC when the speaker is assigned incorrectly. The change from DC to M-DC can be easily achieved by rewriting just one term in the loss function of DC, without any other modifications to the network architecture or model parameters. As such, our method has high practicability because it does not affect the original inference part. The experimental results show that the proposed method improves the performances of the original DC and its expansion method.