  We present a new method to construct integration-by-part (IBP) identities
from the viewpoint of differential geometry. Vectors for generating IBP
identities are reformulated as differential forms, via Poincar\'{e} duality.
Using the tools of differential geometry and commutative algebra, we can
efficiently find differential forms which generate on-shell IBP relation
without doubled propagator. Various $D=4$ two-loop examples are presented.
