  Mutually unbiased bases (MUB) have many applications in quantum information
processing and quantum cryptography. Several complex MUB's in $\mathbb{C}^d$
for some dimension $d$ and with larger size have been constructed. On the other
hand, real MUB's with larger size are rare which lead to consider constructing
approximate MUB (AMUB). In this paper we present a general and useful way to
get real AMUB in $\mathbb{R}^{2d}$ from any complex AMUB in $\mathbb{C}^d$.
From this method we present many new series of real AMUB's with parameters
better than previous results.
