According to Wikipedia:

The Byzantine calendar was identical to the Julian calendar except that:

the names of the months were transcribed from Latin into Greek;
the first day of the year was September 1, so that both the ecclesiastical and civil calendar years ran from 1 September to 31 August, (see Indiction), which to the present day is the Eastern Orthodox church year;
dates were seldom, if ever, reckoned according to the kalends (καλανδαί, kalandaí), nones (νωναί, nōnaí), and ides (εἰδοί, eidoí) of the months in the Roman manner, but simply numbered from the beginning of the month in the Greek, Syrian, and Egyptian manner, and,
its era was based on the year of creation, reckoned September 1, 5509 BC, to August 31, 5508 BC, rather than the foundation of Rome; years were also reckoned by their place in the indiction and not by the years' consuls.

The leap day of the Byzantine calendar was obtained in an identical manner to the bissextile day of the original Roman version of the Julian calendar, by doubling the sixth day before the calends of March, i.e., by doubling 24 February.

Months names:

Ἰανουάριος;
Φεβρουάριος;
Μάρτιος;
Ἀπρίλιος;
Μάϊος;
Ἰούνιος;
Ἰούλιος;
Αὔγουστος;
Σεπτέμβριος;
Ὀκτώβριος;
Νοέμβριος;
Δεκέμβριος

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Byzantine calendar #4868

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