  In a base phi representation a natural number is written as a sum of powers
of the golden mean $\varphi$. There are many ways to do this. Well known is the
standard representation, introduced by George Bergman in 1957, where a unique
representation is obtained by requiring that no consecutive powers $\varphi^n$
and $\varphi^{n+1}$ do occur in the representation. In this paper we introduce
a new representation by allowing that the powers $\varphi^0$ and $\varphi^1$
may occur at the same time, but no other consecutive powers. We then argue that
this representation is much closer to the classical representation of the
natural numbers by powers of an integer than Bergman's standard representation.
