The invention relates to an unbonded flexible pipe with a longitudinal axis and which comprises from inside outwards a carcass formed by metal windings with gaps between neighboring windings, at least one covering tape and an inner sealing sheath of a polymer extruded onto the covering tape. The covering tape is helically wound with a winding direction defining a tape length direction and a tape width direction perpendicular to the tape length direction. The covering tape comprises lengthwise continuous filament yarns arranged in the tape length direction of the covering tape. The covering tape has a thickness direction perpendicular to the tape length direction. The warp yarns have a thickness determined in the thickness direction of the covering tape of about 100 μm or less, such as of about 50 μm or less, such as from about 5 to about 25 μm.