  We give a construction of a real number that is normal to all integer bases
and continued fraction normal. The computation of the first n digits of its
continued fraction expansion performs in the order of n^4 mathematical
operations. The construction works by defining successive refinements of
appropriate subintervals to achieve, in the limit, simple normality to all
integer bases and continued fraction normality. The main diffculty is to
control the length of these subintervals. To achieve this we adapt and combine
known metric theorems on continued fractions and on expansions in integers
bases.
