Transcatheter valve prosthesis

A method for implanting a replacement valve in a patient's heart, comprising:

• advancing an elongate outer member from a first delivery catheter to form a loop around native valve leaflets and/or chords with the elongate outer member;
• partially deploying from a second delivery catheter a radially self-expandable tubular body having an inflow end and an outflow end, a valve disposed within a lumen of the tubular body, and a preformed groove disposed at an outer surface of the tubular body between the inflow end and the outflow end, the preformed groove having a circumferential opening facing radially outward of the tubular body, such that, when the tubular body is partially deployed, the tubular body is inside the loop, the outflow end but not the inflow end is deployed from the second delivery catheter, and the tubular body includes a frustoconical shape that slopes radially outward from the preformed groove toward the outflow end;
• and
• moving the loop into the preformed groove through the opening.