  By using a jump transformation associated to the Romik map, we define a new
continued fraction algorithm called odd-odd continued fraction, whose principal
convergents are rational numbers of odd denominators and odd numerators. Among
others, it is proved that all the best approximating rationals of odd
denominators and odd numerators of an irrational number are given by the
principal convergents of the odd-odd continued fraction algorithm and vice
versa.
