Brainteasers

[appolose]

Johann said:

Ok, I hope this one sticks:

A ninja is trying to get in a building that only has one floor. The building has a total of 16 rooms, which are all square shaped and all of the same size (seen from above, the biulding has the shape of a square). All of the rooms have guards in them and are all conected to each other through soundproof doors. There are only two ways into the building: the most northwest room and the most southeast room. The guard in the most northwest goes out for a smoke and the ninja swoops in and kills him. When he enters the room where the guard was the door locks behind him, so he can`t get out of the building. His mission is to kill every single guard without ever going back to the murder scenes and still escape the building. How will he do that?

PS.: Sorry for bad english :)

I don't suppose that he could pass through a room without killing a guard, could he (ninja stealth)?  That way he could return to a room without returning to a murder scene!