We prove that if f ( z ) is a continuous real-valued function on ℝ with the properties f ( 0 ) = f ( 1 ) = 0 and that ‖ f ‖   z   = inf x , t | f ( x + t ) − 2 f ( x ) + f ( x − t ) / t | is finite for all x , t ∈ ℝ , which is called Zygmund function on ℝ , then max x ∈ [ 0 , 1 ] | f ( x ) | ≤ ( 11 / 32 ) ‖ f ‖ z . As an application, we obtain a better estimate for Skedwed Zygmund bound in Zygmund class.