He later moved to Tampico where he formed the Cuarteto Tamaulipeco with composer Ernesto Cortázar.
After two of the members were fatally injured in an automobile accident, Barcelata returned to Mexico.
His most famous song is "María Elena", (also known as "Yours is My Heart"), and was originally written for Lucia Martínez García.
Shortly before registering the song, Barcelata showed it to his businessman friend Anacarsis "Carcho" Peralta, who loved it; curiously, the song appeared shortly afterwards as "María Elena", the name of one of the businessman's girlfriends.
In 1958, the Brazilian group Los Indios Tabajaras recorded a version that became popular throughout Latin America and later (in 1963) reached the No.
In total, he left behind a catalog of 214 songs, including "Por ti aprendí a querer", and "El Cascabel", among others.