Float Crew was changing out a 7' long 20"" exp. joint on matrix pump. Bolt holes were not lining up on flanges. Float Crew Leaderman(FCL) used a lifting strap as choker around exp. joint. FCL tightened down on strap & signaled operator to hoist up. As operator started hoisting, the strap broke. FCL left hand was still on strap causing it to suddenly shift.