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Developing mechanical metamaterials with programmable properties is an emerging topic receiving wide attention. While the programmability mainly originates from structural multistability in previously designed metamaterials, here it is shown that nonflat‐foldable origami provides a new platform to achieve programmability via its intrinsic self‐locking and reconfiguration capabilities. Working with the single‐collinear degree‐4 vertex origami tessellation, it is found that each unit cell can self‐lock at a nonflat configuration and, therefore, possesses wide design space to program its foldability and relative density. Experiments and numerical analyses are combined to demonstrate that by switching the deformation modes of the constituent cell from prelocking folding to postlocking pressing, its stiffness experiences a sudden jump, implying a limiting‐stopper effect. Such a stiffness jump is generalized to a multisegment …