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Self-attention models have achieved state-of-the-art performance in sequential recommender systems by capturing the sequential dependencies among user-item interactions. However, they rely on positional embeddings to retain the sequential information, which may break the semantics of item embeddings. In addition, most existing works assume that such sequential dependencies exist solely in the item embeddings, but neglect their existence among the item features. In this work, we propose a novel sequential recommender system (MLP4Rec) based on the recent advances of MLP-based architectures, which is naturally sensitive to the order of items in a sequence. To be specific, we develop a tri-directional fusion scheme to coherently capture sequential, cross-channel and cross-feature correlations. Extensive experiments demonstrate the effectiveness of MLP4Rec over various representative baselines upon two benchmark datasets. The simple architecture of MLP4Rec also leads to the linear computational complexity as well as much fewer model parameters than existing self-attention methods.