Xiaomi announced the newest version of MIUI back in July along with the release in China of the Mi 5X, and then went on to release multiple MIUI 9 Global Beta ROMs for many devices. After months of beta testing for the Global version, the Chinese OEM announced the stable version of MIUI 9 on November 2 alongside the release of the Redmi Y1. Xiaomi stated that the roll-out would be a staged one; the first few devices to get the update would be the Redmi Note 4, the Mi Mix 2, the Mi Max 2, and the Redmi Y1; and every other Xiaomi device released since 2012 would get the update in December.

Even before the announcement, some Mi 6, Mi Mix 2 and Mi Max 2 users were getting the OTA update notification for MIUI 9. On the same day of MIUI 9 Global's announcement, Xiaomi released the Beta Stable update for the Redmi Note 4. This meant that the update would only roll-out to a random set of users. Those users would have the chance to report bugs, and if no major bugs were reported, the company would give the same ROM the 'Global Stable' nomenclature within a few days.

The 'Global Stable' nomenclature means that the update is stable and will roll-out to all users. Xiaomi has now released the MIUI 9 Global Stable update for the Redmi Note 4 Snapdragon variant (also known as the Redmi Note 4X in some markets). The ROM is now available for flashing via both fastboot and recovery methods.

The update does not change the underlying Android OS version, which still remains at Android 7.0 Nougat. This means that despite being the first device to be updated to MIUI 9 Global, the Redmi Note 4 still does not have Android 7.1. It is worth noting that MIUI 8 for the Mi Max 2 and the Mi Mix 2 was based on Android 7.1 Nougat.

The full changelog for the update for the Redmi Note 4 is stated below:

Users can wait for the OTA update to arrive to their phones, or download the ROM in fastboot or recovery version from the source link.

Source: MIUI Forums