The eastern stitch is an interesting one that can add texture in the worked area. An interesting variation is when you can include a bead to it. If worked on even weave cloth, it can be used a filling stitch too. Here, I will illustrate the simple stitch technique of this stitch. It resembles closely to the sorbello stitch , the reason why I listed this under the Palestrina family of stitches.

This stitch works from left to right. I will work between two parallel stitch lines.

eastern_stitch_1 eastern_stitch_2
Fig 1: Start by stitching A-B. Come out from C, in through A again, and then out from D.  Fig 2: Pass the needle under C-A without plucking the fabric underneath. 
eastern_stitch_3 eastern_stitch_4
Fig 3: Now, pass the needle under A-B without plucking the fabric underneath.  Fig 4: Pull the needle out and you will see a nice pattern emerge. Take the needle in through D to finish off the stitch.
eastern_stitch_5 eastern_stitch_6
Fig 5: A single stitch looks like this. You can make individual stitches like this with spaces or scattered about.
Fig 6: You can also make a row of closely made eastern stitches as shown. Just keep the stitch points B and D of the previous stitch connected to A and C of the next stitch.