The 24-year-old was given the boot after project managing the losing side in a shopping channel task.
Sir Alan Sugar, 62, thought Howard wasn't offering enough to teammates Kate Walsh and Lorraine Tighe.
'I haven't got time for just ordinary people,' he said as he gave Howard the chop.
Debra Barr, James McQuillan and Yasmina Siadatan also remain in the competition to battle it out with Kate and Lorraine.
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