Is there a Mutex in Java?

Is there a Mutex object in java or a way to create one? I am asking because a Semaphore object initialized with 1 permit does not help me. Think of this case:

try {
   semaphore.acquire();
   //do stuff
   semaphore.release();
} catch (Exception e) {
   semaphore.release();
}

if an exception happens at the first acquire, the release in the catch block will increase the permits, and the semaphore is no longer a binary semaphore.

Will the correct way be?

try {
   semaphore.acquire();
   //do stuff
} catch (Exception e) {
   //exception stuff
} finally {
   semaphore.release();
}

Will the above code ensure that the semaphore will be binary?