Actually, Fernando de Noronha isn't a state — it was a territory between 1942 and 1988 (with status similar to a US unorganized territory), being since then a Pernambuco state district (the only state district in Brazil). Also, a great part of the archipelago constitutes the Fernando de Noronha National Park. Since 1982, the archipelago has been using this flag:
The flag is complicated, the blazon isn't heraldically a true coat of arms and there are many writings, including a silly lettering in Latin: "Fernandi Noronhae" (Fernando de Noronha (sic) discovered the islands and held the brazilwood royal monopoly between 1501 and 1504). Being this flag very accepted as a symbol of the islands, I tried to change it the least possible. I made two variants:
Before explain the changes, I'll explain what I kept: a landscape of main island, including its "great rock" and the dolphins — apart from having some of most heavenly beaches in the world (with excellent options to surf, snorkeling or just sea bath), it's considered the best point of dolphin-viewing of the world.
The first proposal shows the landscape in a circle, with the pair of dolphins being used as a kind of "supporters". I prefer this one, because its designis clearer and, for me, resembles more the Brazilian national flag. The second, although, is more "natural" because shows the dolphins as part of the landscape, diving in the sea.
Other change was the inversion of green shades: I'm sure the mountain is greener than the sea. A problem these flags still have is the different shades of blue and green, that I couldn't solve satisfactorily.
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Before somebody ask: no, I never was in Fernando de Noronha... so far.