F-4	http://www.hoyaenglish.com

The F-4 visa is the overseas Korean visa, or the "Gyopo" visa. F-4 eligiblity is open to overseas Koreans who are citizens of Western countries and whose parents are also citizens of said country, having renounced Korean citizenship after 1948.
F-4 visa holders -- commonly called "Gyopos" or overseas Koreans -- are Korean permanent residents with virtually the same rights as Korean citizens -- with some limitations (unable to obtain credit, for example). Eligibility is open to any overseas Korean who possesses foreign nationality, whose parents surrendered Korean nationality after 1948, i.e., they emigrated out of Korea and became citizens of a different country after the formation of the Republic of Korea (1948), and can provide documentation to this effect (Hojujok, proof of foreign citizenship, proof of parents' foreign citizenship. This type of visa allows an indefinite stay in Korea with unlimited renewals every two years, with virtually unlimited rights of employment, business ownership and property ownership. (The only limitation is that F-4 visa holders cannot work in unskilled labor jobs. They must be employed in professional occupations, i.e., "white-collar jobs", e.g., teacher, businessman, etc.) Also, OAKs (Overseas Adopted Koreans) and half-Koreans who are citizens of a foreign country are eligible as well, as long as they can provide the aforementioned documentation. (OAKs can have surrogate Hojujoks, i.e., family registries, issued by their adoption/placement agency in Korea.)

  A Korean foreigner who had Korean citizenship before his/her obtaining a foreign nationality:
•Passport • Visa application form • A $75.00 of visa fee( Money order, bank cheque or cash) • Substantiating documents for an applicant's ex-Korean nationality such as a Korean family tree register • Substantiating documents for the reasons and the time of obtaining a foreign nationality (certificate of citizenship)
  An immediate family member of a Korean-foreigner who obtained foreign nationality
• Passport • Visa application form • A $75.00 of visa fee( Money order, bank cheque or cash) • Substantiating documents that prove his/her parent's ex-Korean nationality • Substantiating documents for the reasons and the time of the obtaining foreign nationality of the applicant and his/her parent (certificate of citizenship) • Substantiating documents which establish the relationship of the family such as a certificate of birth

Please call your Designated Korean Consulate for more details.