Borrowing a technique due to Ando-Li-Mathias, we define a geometric 
mean of $(k+1)$ (positive invertible) operators from that of $k$ (or a $k$-tuple of)
operators with a parameter $\lambda \in (0,1]$. If $\lambda = 1,$ 
then the corresponding geometric mean $G_{\l}(=G_1)$ of $(k+1)$ 
operators is one defined by Ando-Li-Mathias, and if $\lambda = 2/3,$ 
then $G_{\l}$ is one given by one of the authors in the preceding paper. 
We also show that a formula due to Yamazaki of the geometric mean 
for a $3$-tuple of $2 \times 2$ matrices satisfying a trace condition does not 
depend on any choice of a parameter in construction.