Expedition 51 Commander Peggy Whitson and Flight Engineer Jack Fischer of NASA also installed a pair of antennas on the station on May 23 to enhance wireless communication for future spacewalks.
Spacewalkers have now spent a total of 1,250 hours and 41 minutes working outside the station during 201 spacewalks in support of assembly and maintenance of the orbiting laboratory.
This was the 10th spacewalk for Whitson, who moves into third place all-time for cumulative spacewalking time, and the second for Fischer.
ISS programme managers decided to press ahead with the spacewalk after a review of preparations and crew readiness on Sunday.
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The data relay box is one of two systems housed in the truss that control the functionality of radiators, solar arrays, cooling loops and other station hardware.
The other MDM in the truss was functioning perfectly, providing uninterrupted telemetry routing to the station's systems.
A similar MDM replacement spacewalk was conducted in April 2014 by Expedition 39 crewmembers Steve Swanson and Rick Mastracchio.