I have been searching for possibility to travel from Montreal to Melbourne via Singapore. At both the two destinations I want to stay for about a month. As a Star Alliance member, United offers a 75000 points flight from N America to Australia. An open jaw is allowed. If I find my own way from Melbourne to Singapore, and hook up with United for my return from Singapore to Montreal, is that considered an open jaw? United offers no flight between Sin and Mel.

Thanks in advance.