Jyotish describes the term HORA in different contexts. Planetary rulers of (roughly) each hour from sunrise used for consideration in bala computation, the hora lagna oriented chart etc. This communication is about the Hora varga, one of the divisional charts also known as V-2 or D-2 which is associated with wealth or sampatti.
For a long time, and even today by far and large, this chart has simply two signs, leo and cancer ruled by sun and moon with the planets all lumped into these two signs based on their location in the kshetra (lagna-rashi) chart (the natal chart) and the gender of the sign and the gender of the two halves within each masculine (odd) and feminine (even) sign. Then, it is mostly left aside though faithfully appears in all printouts etc, like the shy bride who is brought along by the husband to the party celebration and then quietly sits next to her husband without opening her mouth! (I must express my gratitude to Shri K.N. Rao who used a similar analogy for the navamsha chart in his incredibly brilliant writings and which made me roll on the floor laughing at the brilliant analogy presented by this unique great jyotishi!

)
I think several variants have been suggested by more inclusive jyotishis. The first one I read long ago was in The Astrological Magazine in early 80s if I recall correctly in which alternatives were suggested for hora, trishamsha and drekkana and other vargas. I believe there have been others too.
The bipolar treatment (no pun intended!) that is seen in most printouts (two horas - karka and simha) arises obviously from the reference in (for example, BPHS) where the two horas or groups of moon and sun are mentioned. But then there is also the reference to 'cycles' of the signs (meshadi...).
Odd signs have first half belonging to masculine and second half belonging to feminine signs. The reverse is true for even signs.
There are two ways of dealing with this, one being to run the cycle (aries, taurus, gemini...) for groups of odd signs as a class, and even signs as another cluster. So the order could be:
Aries: Aries, Taurus
Gemini: Gemini, Cancer
Leo: Leo, Virgo
...
Taurus: Taurus, Aries
Cancer: Cancer, Gemini
Virgo: Virgo, Leo
But this looks counter-intuitive and complex and introduces a bias or potential bias -- The first part of any sign then becomes like vargottama with the kshetra and D2 having the same quality. CAVEAT: Vargottama is generally recommended only for V9. I am NOT suggesting that we should extend that to other vargas!
The other series is more attractive (to me, anyway!)
Aries: Aries, Taurus
Taurus: Cancer, Gemini
Gemini: Leo, Virgo
and so on...
If you wish to experiment with this, at your own risk of course (!), my advice would be to not over-apply this and only to focus on the sector related to wealth, sampatti as understood in the worldly sense. At least at first...!
Love, Light, Learning (NOT teaching!),