Flying Blind

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Flying Blind is a mystery novel by Max Allan Collins that was first published in 1999. The book was part of Collins' ongoing series of novels featuring private detective Nathan Heller.
In the Heller series, the lead character is frequently featured interacting with historical figures of the 1930s and 1940. In Flying Blind, set in the mid-1930s, Heller is hired by book publisher and publicist George P. Putnam to act as a bodyguard for his wife, strong-willed celebrity aviator Amelia Earhart, and at the same time investigate who might be sending her threatening letters.
Heller is initially reluctant to act as a "babysitter" and he and Earhart have a rocky relationship at first, but eventually their relationship progresses to the point where they become lovers.