Is it possible to simulate a fair coin with a finite number of tossing of a biased one?

Question

It is a classic problem to simulate a fair coin with a biased one.

According to Fair Coin (wiki),

John von Neumann gave the following procedure:

1. Toss the coin twice.
2. If the results match, start over, forgetting both results.
3. If the results differ, use the first result, forgetting the second.

In the worst case, the procedure may not terminate.

Problem: Is it possible to design an algorithm which guarantees termination in the worst case? What is the technique to solve such an impossibility problem?