No that is not possible. Since Big-Oh is suppose to be an approximation of the number of operations an algorithm performs related to its domain size then it would not make sense to describe an algorithm as using a negative number of operations.
The formal definition section of the wikipedia article actually defines the Big-Oh notation in terms of using positive real numbers. So there actually is not even a proof because the whole concept of Big-Oh has no meaning on the negative real numbers per the formal definition.
Short answer: Its not possible because the definition says so.
