To make this simple, the definition of "war" that I will be using as defined by the Correlates of War Project is defined as having at least 1000 deaths per year. There have been 38 wars between UN members between 1945 and 2015. This number is excluding extra-state and intra-state wars.

For more information, you can access the datasets on the Correlates of War Project website. There you can access anything and everything about conflict or trade or relationships from 1815 to 2005

38

Do you mean UN vs UN or at least one member was a UN member?