Yes you're correct! The Jacobite succession went as follows (the numbers reflect English & Scottish thrones, ie James II (England) and VII (Scotland):
James II and VII (1685 - 1701) [third son of King Charles I and of his wife, Princess Henrietta Maria of France he was overthrown by William of Orange and James's daugher (by his 1st marriage) Mary thus starting the controversy when they said his son James (by his 2nd wife Princess Maria of Modena) was a changeling] to his son
James III and VIII (1701 - 1766) to his son
Charles III (1766 - 1788) aka 'Bonnie Prince Charlie' to his brother
Henry IX and I (1788 - 1807) [who was actually a high-ranking Cardinal in the Catholic Church; he is buried at St Peter's Basillica in Rome; after his death, his executor Monsignor Cesarini sent the Hereditary Prince of Hanover (later the Elector George IV) several jewels from Henry's private collection including a Lesser George (thought to have been worn by Charles I at his execution, and now at Windsor ), a St. Andrew's Cross (now at Holyrood Palace in Edinburgh), and a ruby ring.]
Charles IV (1807 - 1819) [ He was the eldest son of Vittorio Amadeo di Savoia, Duke of Savoy (later Victor Amadeus III of Sardinia) and Infanta Maria Antonia of Spain (daughter of Philip V of Spain). Because of the lack of heirs, the 'succession' went back to the great-great-grandson of Henrietta Anne, youngest daughter of King Charles I father of James II] to his brother
Victor Emanuel I of Sardinia, Victor I (1819 - 1824) to his daughter
Maria Beatrice (wife of Francesco IV, Duke of Modena who was her uncle, yuck) to her son Mary III and II (1824 - 1840)
Francesco V, Duke of Modena Francis I (1840 - 1875) to his niece (daughter of his brohter Archduke Ferdinand of Austria-Este)
Maria Theresia, wife of Ludwig III of Bavaria Mary IV and III (1875 - 1919) to her son
Rupprecht, Robert I and IV (1919 - 1955) then to his son,
Duke Albrecht, Albert (1955 - 1996) followed by his son
Duke Franz Francis II (1996 - present)