Correct you just don't get the free attack that the Improved Trip gives you normally when you succeed on a trip attempt.
I.e you get
Attack - (10 damage)
Knockdown Trip (Free)
Not
Attack (10)
Knockdown (Free)
Improved Trip regular melee attack (free)
Comes from this:
Improved Trip [General]
Prerequisites
Int 13, Combat Expertise.
Benefit
You do not provoke an attack of opportunity when you attempt to trip an opponent while you are unarmed. You also gain a +4 bonus on your Strength check to trip your opponent.
If you trip an opponent in melee combat, you immediately get a melee attack against that opponent as if you hadn’t used your attack for the trip attempt.