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A function g : R → R from the real line to itself is called a right B1 compositor if for any Baire class one function f : R → R, f ◦ g : R → R is Baire class one. In this study, we first apply Jayne-Rogers Theorem [2] to prove that every right B1 compositor is D-continuous where D is the class of all positive functions on R and thus give a positive answer to a problem posed by D. Zhao. This result then characterizes the right B1 compositor as a class of naturally defined functions. Furthermore, we also improved some of the results in [4]. Lastly, a counterexample was constructed to a claim in [4] that every function with a finite number of discontinuity points is left B1 compositor.

<i>K</i>-CONTINUOUS FUNCTIONS AND RIGHT <i>B</i><sub>1</sub> COMPOSITORS