After killing the two assassins in the first of the THREE CONNECTED ROOMS WITH DECORATED COLUMNS, instead of proceeding to the switch in the THIRD (SOUTH) ROOM, you can use the bars on the ceiling of the first room to reach the elevated doorway in the middle of the south wall.

Go through the small connecting room to the doorway overlooking the MIDDLE ROOM.

Now move onto the small, square ledge on the left by running across the gap at the corner where the ledge meets the doorway. Be careful not to run on off the edge. Then take a running jump to the next ledge.

While standing here, sidestep to the left corner and turn to face the narrow pillar with eh dark stone ball sitting on top of it.

Equip the shotgun, hold the Look button, and lean back so Lara's torso is roughly level with the ball.

Shoot the ball to knock it down, making a hole in the floor.

NOTE: If you don't have shotgun ammo, you can deal with the assassin lurking below, drop down, and get some from the low block. Then go back into the first room, climb back up, and try again. Or use the alternate shortcut shown below.

- OR -

From the ledge shown in the screenshot above, turn to the west to face the open trapdoor. Jump straight up to grab the overhead bars. Then monkey swing toward the trapdoor.

Swing forward as far as you can, so Lara's chest and legs disappear into the trapdoor.

Then let go and quickly press Action again to grab the ledge below the open trapdoor. Pull up through the trapdoor. Now pick up the main walkthrough here, with the paragraph that begins, "Turn back toward the (west) wall and pick up the Uzi clips at one end of this ledge."

[Great Hypostyle Hall Walkthrough]