Here's How

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  Step 1: Using spirit level, draw a horizontal line across 12 palings, just under top rail. Draw another line, the same length, just above bottom rail (note that lines may not be parallel to rails).
• Step 2: Mark these lengths on 90 x 45mm treated pine and cut to make gate supports.
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  Step 3: Affix gate supports, flush with top and bottom lines, using a 50mm treated pine screw at each end.
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  Step 4: To make bracing, mark a centre line on each gate support. Hold length of 90 x 45mm treated pine against supports on centre mark at bottom, and at bottom left corner of top support. Mark in angle at each end, then repeat for right side.
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  Step 5: Cut angles at ends of bracing. Rest in position on fence and mark in a plumb-cut on each brace, 20mm from centre where they meet. Cut off triangles. This allows space for bottom bolt to be installed later. Affix bracing to fence with evenly spaced 50mm screws.
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  Step 6: Using the centre marks, mark plumb centre lines on top and bottom fence rails, squaring off gate supports which you know are level.
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  Step 7: Drill tight clearance holes through top and bottom rails, and gate supports, at these positions, using centre lines as a guide to keep drill straight. You may need to gently tap fence palings away from rails to give space for your drill to align correctly. Repeat for top and bottom
  gate supports.
• 
  Step 8: Feed 12mm bolt and 2 washers through top rail and top gate support. Wind a washer and nut onto end of bolt. Apply a drop of Loctite to bolt and finish tightening. Repeat this process for bottom of gate. If the lengths of bolts are too short, you may need to counterbore a shallow, wider hole with a Speedbor bit, on top and bottom rails to allow for washer and bolt.
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  Step 9: Attach 1 barrel bolt, at child height, on your side and your neighbour’s side of the fence and gate, so it can be locked from either.
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  Step 10: Working on other side of fence, drive 40mm stainless-steel screws in top and bottom gate supports on each paling.
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  Step 11: To mark in level cutting lines, use a straightedge in gaps between palings to mark position of top of top gate support, and underside of bottom support. Check they’re level.
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  Step 12: Set saw depth to suit palings, then plunge-cut along both lines. Finish ends of cuts with a handsaw to release gate. If necessary, adjust height of gate using top bolt and nut.