A 1961 map of the border between British Honduras (now Belize) and Guatemala
Click here for a larger version of this map.
The Belize–Guatemala border is the line almost straight with 266 km long, almost towards the 89th meridian west, which separates the west of Belize's territory from Guatemala's. It begins at the tri-border Belize-Guatemala-Mexico, running directly south to Garbutt's Falls near Melchor de Mencos. From there, it runs further south to Gracias á Dios Falls, and then follows the Sarstoon River east to the Caribbean at the Bay of Amatique.* The border runs along the south side of Sarstoon Island.** In Guatemala it borders the Department of El Petén and Belize districts are the border Orange Walk, Cayo and Toledo.
This border was delimited by the Wyke–Aycinena Treaty in 1859,** but there were disputes over the rest of the nineteenth century and also in the twentieth century, with the participation of the United States of America and the United Kingdom. The situation was partially resolved in 1991 when Guatemala officially recognized Belize's independence and diplomatic relations were established.
The main problem now is the Guatemalan constitution still includes Belize as part of Guatamala.
If any Guatemalan official tries to suggest changing the words in the constitution, he will be branded as a traitor, so they cant change their constitution regarding Belize.
But if the ICJ or International body orders Guatamala to change their constitution, then it can be changed, without anyone being branded as a traitor.
All the maps I have found, confirm the border follows the deep water channel, to the south of Sarstoon Island.
References
* Aycinena-Wyke Treaty (PDF), 1859
** Ministerio de Relaciones Exteriores de Guatemala. "Histórica del Diferendo Territorial" (PDF) (in Spanish).
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