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At the northwest corner of the map, you'll find your first Fragment on a pole above a little enclosed courtyard.
Head south of where you found the first fragment, along Galata's western wall, and the next one will be waiting for you on top of a pole jutting out of the water.
The next Fragment is due east of the last one, on the eastern side of the wall below:
To grab it, use the staircase pictured below to start climbing.
You'll find this Fragment on a little chimney to the southwest of Galata Tower.
This one's a straight shot southeast from Fragment 4, clearly visible on an awning. You'll actually pass this one early in the story, when Yusuf teaches you to use the hookblade.
Head up the street northeast of the last Fragment, and you'll find this one on the rooftops, atop another little chimney.
Head northwest, over the wall adjoining Galata Tower, and you'll find the next Fragment sitting on top of a signpost:
This one's a tricky bastard. You can see it if you're looking at Galata Tower's eastern face, on an isolated platform. There are no clear means to climb up to it, and trying to drop down onto it from above just results in a Leap of Faith into a waiting haystack.
Reaching it is simpler than it looks, though; just climb up Galata Tower's north face until you're sure you're well above the platform. This is a pretty good stopping place:
Now, leap off to the east and deploy Ezio's parachute. After that, it's just a matter of floating down to the platform without overshooting it.
Head southeast of Galata Tower, and you'll see the next Fragment on top of another chimney, just west of a bank.
Head over to the northeastern edge of Galata, and you'll see the next Fragment on top of an archway, next to a couple of rickety non-roofs.
To find Galata's last Fragment, head to the lighthouse at the southeastern corner of the district. You'll know you've found the right one if it looks like this.
Climb up to the top, and you'll be stopped by an impassable fence. No problem, though; just inch around the ledge until you see the next Fragment on a tiny outcropping beneath you. Drop down, and it's yours.