Samsung Galaxy Note 4 has a history of not playing well with other wearable devices like the Fitbit Charge HR. Unfortunately the Xiaomi Mi Band also falls into this Do Not Use category.
Finding and installing the Mi Fit App on Google Play is easy enough. This App is needed to connect your smartphone to the Mi Band
After you have logged into your Xiaomi Account, you are ready to click on No Mi Band associated with this account in order to go to the Mi Band settings to start pairing to the Galaxy Note 4.
Unfortunately, the Galaxy Note 4 will search for the Mi Band but end up not finding it repeatedly.
If you want other smartphones that work with the Xiaomi Mi Band, check out the Sony Z3+, Z4, and Z5 phones as well as Xiaomi's own Mi Note Pro.