The cosmic infrared background (CIB) is a powerful probe of large-scale structure across a very large redshift range, and consists of unresolved redshifted infrared emission from dusty galaxies. It can be used to study the astrophysics of galaxies, the star formation history of the universe, and the connection between dark and luminous matter. It can furthermore be used as a tracer of the large-scale structure and thus assist in de-lensing of the cosmic microwave background. The major difficulty in its use lies in obtaining accurate and unbiased large-scale CIB images that are cleaned of the contamination by Galactic dust. We used data on neutral atomic hydrogen from the recently released HI4PI Survey to create template maps of Galactic dust, allowing us to remove this component from the Planck intensity maps from 353 to 857 GHz for approximately 25% of the sky. This allows us to constrain the CIB power spectrum down to ℓ 70. We present these CIB maps and the various processing and validation steps that we have performed to ensure their quality, as well as a comparison with previous studies. All our data products are made publicly available, 4 thereby enabling the community to investigate a wide range of questions related to the universe's large-scale structure.