Title: Neural Systematic Binder. Abstract: The key to high-level cognition is believed to be the ability to systematically manipulate and compose knowledge pieces. While token-like structured knowledge representations are naturally provided in text, it is elusive how to obtain them for unstructured modalities such as scene images. In this paper, we propose a neural mechanism called Neural Systematic Binder or SysBinder for constructing a novel structured representation called Block-Slot Representation. In Block-Slot Representation, object-centric representations known as slots are constructed by composing a set of independent factor representations called blocks, to facilitate systematic generalization. SysBinder obtains this structure in an unsupervised way by alternatingly applying two different binding principles: spatial binding for spatial modularity across the full scene and factor binding for factor modularity within an object. SysBinder is a simple, deterministic, and general-purpose layer that can be applied as a drop-in module in any arbitrary neural network and on any modality.  In experiments, we find that SysBinder provides significantly better factor disentanglement within the slots than the conventional object-centric methods, including, for the first time, in visually complex scene images such as CLEVR-Tex. Furthermore, we demonstrate factor-level systematicity in controlled scene generation by decoding unseen factor combinations.