Step 1 Open jump rings and set aside for use later. Step 2 Slide four jump rings onto one open jump ring (shown in red). Close the jump ring. Step 3 Add a second red open jump ring through the same four closed jump rings. Split the jump rings into pair as shown in the illustration. Step 4 Attach a paperclip or a head pin through the two end jump rings. That will help you to pick up the jump rings chain more easily.

1. Byzantine chain maille tutorial
from www.zacoo.com
Step 1 Open jump rings and set aside for use later.
Step 2 Slide four jump rings onto one open jump ring (shown in red). Close the jump
ring.
Step 3 Add a second red open jump ring through the same four closed jump rings.
Split the jump rings into pair as shown in the illustration.
Step 4 Attach a paperclip or a head pin through the two end jump rings. That will
help you to pick up the jump rings chain more easily.
Step 5 Flip the two blue jump rings to the direction of the jump rings at the
beginning (shown in black).
Step 6 Push the last two jump rings (shown in red) apart to form the shape as the
picture shown.

2. Step 7 Attach a jump ring through the two blue jump rings.
Step 8 Continue to add a second jump ring (in red color) that with the same position
as the first one.
Step 9 Add two groups of jump rings (the two blue ones and the two red ones) as
shown in the pictures. We can see that they are the same with that in Step 3 and
Step 4.
Step 10 Repeat Step 5 and step 6 to make a make a new unit of chain maille.
Step 11 Add three more jump rings through the previous two jump rings.
Step 12 Repeat Step 3 and step 6 to make another unit of chain maille until it comes
to your desired length.
Source from: http://www.newfashionbox.com/byzantine-chain-maille-tutorial/