A prosthetic heart valve comprising: a collapsible and expandable annular frame that is configured to be collapsed to a radially collapsed state for mounting on a delivery apparatus and expanded to a radially expanded state inside the body, the frame having an inflow end, an outflow end, and a longitudinal axis extending from the inflow end to the outflow end, the frame comprising a plurality of struts defining a plurality of cells; and a collapsible and expandable valve member mounted within the annular frame; and a collapsible and expandable annular sealing member coupled to the frame such that when the frame is in its radially collapsed state, the sealing member can be placed in a delivery orientation in which the sealing member is radially collapsed and extends from the inflow end of the frame in a direction away from the outflow end of the frame and when the frame is expanded to its radially expanded state, the sealing member is caused to move toward the outflow end of the frame in a direction parallel to the longitudinal axis to an operative orientation in which the sealing member covers at least a portion of the cells of the frame; characterized by a tether having first and second end portions and an intermediate portion extending between the first and second end portions, the first and second end portions being secured to the sealing member at spaced apart locations, and the intermediate portion extending through the frame such that when the frame is in its radially collapsed state, the intermediate portion decreases in length and the first and second end portions increase in length to allow the sealing member to be placed in the delivery orientation and when the frame is expanded to its radially expanded state, the radial expansion of the frame causes the intermediate portion to increase in length and the first and second end portions to decrease in length, which is effective to pull the sealing member from the delivery orientation to the operative orientation. a collapsible and expandable annular frame that is configured to be collapsed to a radially collapsed state for mounting on a delivery apparatus and expanded to a radially expanded state inside the body, the frame having an inflow end, an outflow end, and a longitudinal axis extending from the inflow end to the outflow end, the frame comprising a plurality of struts defining a plurality of cells; and a collapsible and expandable valve member mounted within the annular frame; and a collapsible and expandable annular sealing member coupled to the frame such that when the frame is in its radially collapsed state, the sealing member can be placed in a delivery orientation in which the sealing member is radially collapsed and extends from the inflow end of the frame in a direction away from the outflow end of the frame and when the frame is expanded to its radially expanded state, the sealing member is caused to move toward the outflow end of the frame in a direction parallel to the longitudinal axis to an operative orientation in which the sealing member covers at least a portion of the cells of the frame; a tether having first and second end portions and an intermediate portion extending between the first and second end portions, the first and second end portions being secured to the sealing member at spaced apart locations, and the intermediate portion extending through the frame such that when the frame is in its radially collapsed state, the intermediate portion decreases in length and the first and second end portions increase in length to allow the sealing member to be placed in the delivery orientation and when the frame is expanded to its radially expanded state, the radial expansion of the frame causes the intermediate portion to increase in length and the first and second end portions to decrease in length, which is effective to pull the sealing member from the delivery orientation to the operative orientation.