A new kind of bubble having two stable states for a bias field HBhas been found in thin garnet films. The bubble becomes smaller with increasing HBand disappears abruptly at some critical field . However, it does not collapse at . When HBis lowered, it comes into sight suddenly at another critical field . This means that for HBbetween and the bubble has two stable states, one for a large bubble and the other for an unobservably small bubble. This has been well explained in terms of the stability of bubbles containing a definite number of Bloch lines.