3x3 Step 4

Now that we have all of our edge pieces in the proper positions and oriented correctly, we have (at most) five pieces unsolved: all four corners of the U layer as well as the DRF corner. In this step, we will put each of the U layer corners into the proper position, and that will automatically leave the DRF corner in the correct position. (think about it....)

First, we're going to hold our cube differently than from the previous step. Hold your cube so that the unsolved corner in the D layer is now in the RBD position. Now for each corner you need to postion, there are two steps.

Put any U-layer corner piece that needs to be moved into the UFL position by turning only the U layer. Then, apply the move L D2 L' . (Remember the colors of this piece.)
Move only the U layer so that the location (the "hole") where that piece belongs is in the UFL position. Apply L D2 L' again. You can tell where the piece belongs by recalling the two colors (other than the color of the U face). The hole where your corner piece belongs is the corner between the two edge pieces of those colors.

Now, that piece will be in the correct position. Continue until you have positioned all of the U-layer corners correctly.

Note: Do not try to position the corner from the B layer. Once the four U-layer corners have been placed correctly, the B-layer piece will also be in the correct place. Also, remember that the corners may (and most likely will) be twisted incorrectly. The only goal of this step is to put the pieces into the correct spot.

Example:

This cube is positioned with the unsolved corner of the D layer in the RBD spot. First, you position any wrongly place U-layer corner (in this case, OYB) in the UFL position by adjusting only the U layer.

Then, apply L D2 L'. Now, readjust the U layer so that the spot where the OYB corner belongs (between the blue and orange edges) is in the UFL position.

Apply L D2 L' again and notice that the OYB corner is now between the blue and orange edges like it should be.