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Q:

Transmission is shifting hard between second and third gear. on 2004 Hyundai Tiburon

Rookie cbe0621eac06868b3efe0d8d1d3611e23c60d3114864ea2ec19a68cfbd3eebab
Transmission jerks between second and third gear when accelorationing lightly If your giving it more rpm,s it doesn;t do it.
(1) Answer
Provided the transmisson fluid is up to level, clean and clear, you need to get a transmission specialist or a Hyundai specialist to diagnose it for you. Sounds to me, if the fluid's OK, that you may have a line pressure control problem and it needs to be diagnosed by a pro.
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