for the better
Resulting in a more positive situation or outcome. He has started drinking a lot less, which is definitely a change for the better. Moving overseas was a huge undertaking, but I feel like it was ultimately for the better.
*for the better
to be an improvement. (*Typically: be ~; be a change ~.) A change of government would be for the better. A new winter coat would certainly be for the better.
for the better
Resulting in or aiming at an improvement: Her condition took a turn for the better.