Matthew added a 63 to the 64 she shot in the opening round Thursday and her 15-under 127 total broke the previous 36-hole record by six shots.
That record was held by Inbee Park, the world's top-ranked female golfer who has won her last three starts and has also become the second player in LPGA Tour history to win the year's first three major events.
Park, who will try to become the first player on any tour to win four majors in the same year when she competes in the Women's British Open later this month, was five shots off the lead after 36 holes.
Angela Stanford, who shared the first-round lead with Matthew, shot a 67 at the Grey Silo course and was alone in second at 130. Anna Nordqvist, Ryann O'Toole, Cheila Choi, Belen Mozo and Meena Lee were tied for third at 131.
Park was part of the group at 132 following a 67. Stacy Lewis, a distant second to Park in the world rankings, was tied for 19th at 135.
Swim Week Miami Beach 2014 [PHOTOS]