A tufting machine for creating a cut pile carpet with two pile heights comprises a knife 20 reciprocally mounted and inclined relative to a respective hook assembly to pressurize the knife against the hook assembly. The hook assemblies comprises upper 6 and lower 7 hooks with respective cutting edges 8, 9 at the lower edge and are arranged for selectively directing the yarn onto one of the hooks. The knife 20 has a single cutting edge 21 co-operating with both hooks to cut each loop of yarn seized by the hook assembly with a scissor action. A relief 22 is provided between the knife and the lower hook allowing the knife to clear the lower hook 7 when the cutting edge 21 of the knife 20 approaches the cutting edge 8 of the upper hook. The relief may be provided by a recess extending across the entire width of one side of the knife. Alternatively the relief may be provided by offsetting the upper and lower hooks (see figures 5 and 5A) and a chamfer (41) may be provided on the upper hook to direct the knife onto the upper hook and away from the lower hook. In this embodiment the distal end of the upper hook may be thinned and inclined towards the plane of the lower hook.
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