The remains were discovered on a beach in El Hierro called Arenas Blancas – White Sand in Spanish.
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Guacimara Gonzalez, whose brother Joel called the police after digging up the bones, told local press: “We were on the beach with the family when Joel felt something disturbing him under his towel.
“He thought it was some kind of shell and started digging in the sand with his hands.
“He dug up a jawbone and thinking it was some kind of animal started ripping out other bones, until we realized, when we fell on the skull, that he was human.
“There was also some leftover charcoal. We got scared and called the police.
The bones, found on Saturday, were confirmed to be human after a forensic analysis.
Authorities have not yet confirmed their age and whether they are male or female.
The beach is northwest of El Hierro near the remote town of Sabinosa in the municipality of La Frontera
It is described as the only clear sandy beach on the island.
It is also near a popular wine tasting area.
The news is the latest blow to tourism after eight hotel workers tested positive for coronavirus on the holiday islands of Formentera and Menorca.
The Balearic Islands currently have 14 active outbreaks, with just over 70 people affected, but none are believed to be in serious condition.
In Formentera, five people, who are said to work as maintenance agents, have tested positive.
Three others fell ill in Menorca.
A dozen other people are now on the verge of being tested after coming into contact with them.
Vacationers and hotel workers, whom health officials have refused to identify, have been notified.
Formentera was one of four islands where lockdown restrictions were relaxed before mainland Spain – due to the infection rate deemed lower.
The other three were in the Canary Islands.
Last night, the Scottish government lifted the 14-day quarantine requirement for those arriving from the mainland or the Spanish islands.
The government said the decision was made because of improving infection rates.
Spain is now expected to be added later this week to the list of countries where Scots do not have to quarantine when they return home.
Justice Secretary Humza Yousaf said: “Following this latest review and after carefully considering the potential public health impact of changing the national quarantine exemptions, we are in a position to lift this requirement for those who travel from Spain.
“We are constantly monitoring other countries and where it is clearly proven to be safe, we will add more countries.
“It is clear that the virus has not gone away. He’s still active and he’s still deadly. With the lifting of quarantine restrictions in these countries, that means we need to be even more careful in what we do.