Random-ized Forest: A new class of Ensemble algorithms

It's a known fact that bagging (an ensemble technique) works well on unstable algorithms like decision trees, artificial neural networks and not on stable algorithms like Naive Bayes. The well known ensemble algorithm Random forest thrives on the ability of bagging technique which leverages the'instability' of decisions trees, to help build a better classifier. Even though, random forest attempts to handle the issues caused by highly correlated trees, does it completely solve the issue? Can the decision trees be made more unstable than what random forest does, so that the learner be even more accurate? If trees are sufficiently deep, they have very low bias.