Also mightve been mentioned
After the graduation of the first class of SPARTAN-IIs in 2525, Dr. Halsey began planning for the next wave of Spartans; her efforts, however, ran into problems. There were too few candidates that were in sync with her age restriction protocol and a majority of her funding was going towards MJOLNIR maintenance and construction; leaving little room for continued training efforts. By 2531, the majority of her funds had been diverted and she was forced to postpone the effort indefinitely.[4]
Around six years later, however, it seems that enough candidates within the right age were numerous enough to begin a second class. Six year old Yasmine Zaman was abducted and replaced by a Flashclone just like the Class-Is, and taught in a similar way. She however, died during augmentations.
Another girl, Janissary James, was selected as a suitable candidate for training. However, her father, an ORION Project member known now as "James James", killed the to-be kidnapper.[5]
I still believe Halo:Reach Spartans are Second generation Spartan-II´s.