否定式是在实义动词think前加助动词do,然后助动词按照时态变位并采用否定式（用否定副词not修饰do或者do的变位）,think变成动词原形think,如：
She doesn't think she is beautiful.
应该注意的是,楼主给出的句子是一句复杂句,也就是句子中的某个成分是一个从句,在这里从句是she is beautiful做think 的宾语.
带宾语从句的句子,即使宾语从句想要用否定式,通常也要在主句上用否定来实现.比如：
She is beatiful.这是一句简单句,它的否定式是She is not beautiful.
把这句话作为宾语从句用到She thinks主句中时就是She thinks she is beautiful.
但是,如果要把she is not beautiful用在主句中的话,那么not就要移到主句里变成She doesn't think she is beautiful.
这是通常的表达习惯.说的简单点,也就是不管主句还是宾语从句,只要用到了否定,那么否定副词都放在主句动词上.