Let $T = U \vert T \vert $ be the polar decomposition 
 of a  bounded linear operator on a complex Hilbert space ${\mathcal H}$. 
 $T$  is called a class $A$ operator 
 if $ \vert T\vert^{2} \leq \vert T^{2} \vert$. 
 Recently, M. Ch\=o and T. Yamazaki found an interesting operator transform 
 from a class $A$ operator $T$ to a hyponormal operator $\hat{T}$. 
 In this paper we obtain a more suitable form for $\hat{T}$, 
 and prove Putnam's  inequality for a 
 class $A$ operator,  i.e.,
  $ \Vert \ \vert T^{2} \vert -  \vert T\vert^{2} \ 
  \Vert  \leq \Vert \ \vert T(1,1)\vert - \vert T(1,1)^{*} \vert \ \Vert 
   \leq \frac{1}{ \pi} {\rm meas} \ (\sigma(T))$ where $T(1,1) 
    = \vert T \vert U \vert T \vert$ denotes the 
    generalized Aluthge transform. 
     Also, we study related results.