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i j
A four letter word that starts with J and ends with M: jism.
vaj
There is no English word that starts with I and ends with J. However, there are words that end with J, such as: raj, haj, taj, svaraj, swaraj, you may refer to the related question below for more.
Two letter word with J in them: ja. jo. Note that there are no two (2) letter word that ends with J.