3x3 Step 5

L D2 L' F' D2 F This rotates a corner piece clockwise.
F' D2 F L D2 L' This rotates a corner piece counter-clockwise.

In this step, you twist your remaining corners one pair at a time (one clockwise, and one counter-clockwise).
Important: This step must always be done in pairs. So, if you need to twist 3 corners clockwise, you must rotate one clockwise and another counter-clockwise and fix the last 2 corners by repeating this process.

You should hold your cube so that the two corners that need twisting are in the U layer. Now, turn the U layer so that one of the corners that needs twisting is in the UFL position. Perform the appropriate algorithm listed above depending on which way the piece now in the UFL position needs to be twisted.

Now, it will look like your F2L (first 2 layers) are messed up, but it's only temporary. While leaving the F2L stationary, turn only the U layer so that the other piece that needs twisting is in the UFL postion and perform the algoritm from above that you didn't use the first time. Now, you should see that your F2L have been restored and that your pieces have been twisted. Continue this process as long as you still have improperly twisted corners.

Finally, you may need to adjust the U layer to finish your solve.

Note: An exception occurs when the two pieces that need twisting are diametrically opposed on the cube (i.e. the UFL and BDR corners). If this happens, perform R2 so that both pieces are in the same layer and proceed normally. Then perform R2 again after performing both the clockwise and counter-clockwise twistings to restore the cube to the correct state.

Extra Tip: For a speedier solve and so you never have to overanalyze which way to twist your last corners, always do the moves in the order above (the clockwise twist followed by the counter-clockwise twist).

Example:

This example demonstrates how to twist two corners that are diametrically opposed. First, we perform R2 to put both pieces that need twisting in the U layer.

Then, we notice that the YRB piece is in the UFL corner already. Since this piece needs to be rotated counter-clockwise, we first apply F' D2 F followed by L D2 L' .

Now, we find the other piece that needs twisting (the WGO piece) and put it in the UFL position with U. Then, apply L D2 L' followed by F' D2 F . You see that we're almost done.

You just need to apply U' to line up the R face and apply R2 to undo the R2 that we added at the beginning of the step.