Abstract. Following the release of the version 4 Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP) data products from the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) mission, a new version (version 4; V4) of the CALIPSO Imaging Infrared Radiometer (IIR) Level 2 data products has been developed. The IIR Level 2 data products include cloud effective emissivities and cloud microphysical properties such as effective diameter and ice or liquid water path estimates. Dedicated retrievals for water clouds were added in V4, taking advantage of the high sensitivity of the IIR retrieval technique to small particle sizes. This paper (Part I) describes the improvements in the V4 algorithms compared to those used in the version 3 (V3) release, while results will be presented in a companion (Part II) paper. The IIR Level 2 algorithm has been modified in the V4 data release to improve the accuracy of the retrievals in clouds of very small (close to 0) and very large (close to 1) effective emissivities. To reduce biases at very small emissivities that were made evident in V3, the radiative transfer model used to compute clear-sky brightness temperatures over oceans has been updated and tuned for the simulations using Modern-Era Retrospective analysis for Research and Applications version 2 (MERRA-2) data to match IIR observations in clear-sky conditions. Furthermore, the clear-sky mask has been refined compared to V3 by taking advantage of additional information now available in the V4 CALIOP 5km layer products used as an input to the IIR algorithm. After sea surface emissivity adjustments, observed and computed brightness temperatures differ by less than 0.2K at night for the three IIR channels centered at 08.65, 10.6, and 12.05m, and inter-channel biases are reduced from several tens of Kelvin in V3 to less than 0.1K in V4. We have also improved retrievals in ice clouds having large emissivity by refining the determination of the radiative temperature needed for emissivity computation. The initial V3 estimate, namely the cloud centroid temperature derived from CALIOP, is corrected using a parameterized function of temperature difference between cloud base and top altitudes, cloud absorption optical depth, and CALIOP multiple scattering correction factor. As shown in Part II, this improvement reduces the low biases at large optical depths that were seen in V3 and increases the number of retrievals. As in V3, the IIR microphysical retrievals use the concept of microphysical indices applied to the pairs of IIR channels at 12.05 and 10.6m and at 12.05 and 08.65m. The V4 algorithm uses ice look-up tables (LUTs) built using two ice habit models from the recent TAMUice2016 database, namely the single-hexagonal-column model and the eight-element column aggregate model, from which bulk properties are synthesized using a gamma size distribution. Four sets of effective diameters derived from a second approach are also reported in V4. Here, the LUTs are analytical functions relating microphysical index applied to IIR channels 12.05 and 10.6m and effective diameter as derived from in situ measurements at tropical and midlatitudes during the Tropical Composition, Cloud, and Climate Coupling (TC4) and Small Particles in Cirrus Science and Operations Plan (SPARTICUS) field experiments.