An elevator arrangement includes first and second movable elevator units, the first unit being an elevator car and the second unit being a counterweight, and a roping system including a first roping portion suspending the first and second elevator units, and being locked at least to the second elevator unit, a second roping portion being suspended by the first elevator unit and the second elevator unit, and being locked at least to the second elevator unit. The first and the second roping portions are successive portions of a roping passing unbroken via a locking arrangement provided at the second elevator unit, the locking arrangement locking the roping to the second elevator unit between the first and the second portions. In a method in constructing an elevator, the locking arrangement is unlocked and thereafter the roping is repositioned with respect to the locking arrangement and thereafter the locking arrangement is relocked.