From the last day of August in 2012 until virtually the end of the year, they swept all before them. In chronological order they beat everyone there was to beat in the Guinness PRO12 the first time around - Glasgow Warriors, Ospreys, Munster, Cardiff Blues, Connacht, Dragons, Edinburgh, Zebre, Benetton Treviso, Scarlets and Leinster.
Under a South African captain, former Springbok lock Johann Muller and a Kiwi coach, Mark Anscombe, Ulster reeled off 11 straight wins before losing, 24-10 to Munster at Thomond Park over Christmas.
By then they had transferred their winning domestic habit to Europe, starting with a bonus-point home win over Castres which they duly followed with another, at Northampton to the tune of 25-6.
The trouble with the best of starts is that sometimes they can dissolve into the most anti-climactic of finishes as Ulster supporters know only too well. Their squad's apparent invincibility during the first half of the 2012-13 season made what was to follow all the harder to bear with knock-outs in Europe by Saracens and, worst of all, by Leinster in the PRO12 final at the RDS.
No matter how long their latest winning run lasts, Ulster ought to have no problem staying grounded. The vast majority of their current players will have no need for any lessons in recent history, not least because they were responsible for making it.
A few with longer memories will welcome their next opponents to Belfast on Saturday night with some relish. Ospreys make the trip at the end of a week hammering out the dents caused by a few bumps too many at the RDS in the course of losing their unbeaten record to Leinster.
Nothing that happens this weekend will alter the fact that the Welsh region has a special niche in Ulster history. Ireland's northern province took the PRO12 title for the only time in unforgettable circumstances at Swansea, in May 2006.
They won 19-17 thanks to a long-range David Humphreys drop goal that struck both uprights on its reluctant way over, a goal that clinched the title for his native province, by a single point from Leinster whose retribution can be gauged by three play-off victories in the last four seasons.
Four of that champion Ulster team - Rory Best, Andrew Trimble, Tommy Bowe and Roger Wilson - are still there. Even in that kind of company, Wilson stands out.
He may be unable to contribute more than one of the 231 Ireland appearances made by the quartet as a foursome but Wilson has a longevity which the others, not exactly slouches when it comes to standing the test of time, will be hard pushed to match.
Last week provided reassuring evidence that his powers of endurance show no sign of waning. Two days after turning 35, Ulster's three-dimensional back-row forward officiated at the burial of the Glasgow bogy, a worthy 22-17 win over the Warriors at Scotstoun hoisting the perennial contenders to the top of the pile.
A more significant result during an eventful opening month is difficult to find.
Round 5 features two mighty collisions of the top four. Sixty-five minutes after Ulster-Ospreys gets underway in Belfast, the Blues in second place kick off against Leinster in fourth at the BT Sport Cardiff Arms Park.
Head coach Danny Wilson may well have had Johnny Sexton in mind when he spoke of the Blues' need to improve if they are to make it five wins out of five. Ireland's fly-half having marked his delayed start to the season by puncturing one of two unbeaten Welsh regions, he will now attempt to puncture the other.
The one certainty is that Saturday evening's top two events will have the shuddering impact of excavators let loose on the landscape of the top four. Once the dust settles on the rearranged earth, Munster will hope to ensure they are the chief beneficiaries at the end of a week when their mightiest former player, Paul O'Connell, is otherwise engaged on Ryder Cup duty as part of Europe's motivational team.
Zebre appear at Thomond Park on Saturday encouraged by a near-miss against the Blues last week. A thunderstorm having robbed them of the prospect of a home win over Connacht, they have a good cause for believing they are due a break.
Getting one at Limerick, of all places, is difficult at the best of times. Zebre have lost all eight Guinness PRO12 matches against a Munster team whose bonus point home win over Edinburgh last week pushed them up to fifth.
Glasgow Warriors resume life without acrobatic Fijian Leone Nakarawa in sore need of resuming normal service with nothing more than two losing bonus points to show for narrow reverses against the Blues and Ulster. A swift return to Wales on Friday night takes them to Rodney Parade where the Dragons need to address a few issues of their own after coming to grief in Treviso.
If three successive defeats sounds unthinkable for the Warriors given their status as the most consistent of Guinness PRO12 teams over a five-season stretch, then they need only look at Connacht for proof that it can happen to the best.
After their meteorological reprieve in Zebre the previous week, the champions' failure to turn the tide against the Scarlets leaves them pinned to the bottom, still pointless three matches into the defence of their title.
The more optimistic of the Connacht faithful will have looked at the table and considered that they have given the rest enough of a start. Edinburgh's appearance in Galway on Friday night offers them another chance to get out of the blocks against opponents without a point on the road from trips to Cardiff and Limerick.
Benetton Treviso and Scarlets, both up and running after home wins last weekend, collide at the Stadio Monigo on Saturday towards the conclusion of what ought to be another blood-and-thunder round.
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