That included high level meetings during the leaders' week at the UN General Assembly from 19 September.
In the poll, Portugal's candidate Antonio Guterres remained highest ranked and had picked up 12 'encourages' - one more than in the past two straw polls. He still has two discourages but has topped all four straw polls.
Slovakian Foreign Minister Miroslav Lajcak consolidated his massive leap in the third poll - he remained in second placing with 10 votes in support, four discouraging and one no opinion.
The highest ranked women were Bulgaria's Irina Bokova and Argentina's Susana Malcorra with seven encourages each.
After the last straw poll Foreign Minister Murray McCully and Prime Minister John Key said there was still no reason for Clark to drop out of the race because of the possibility of changes in candidates' fortunes once the vetoes came into play.
Key raised Clark's candidacy with leaders including US President Barack Obama and Russia Prime Minister Dmitry Medvedev at the East Asia Summit in Laos last week.
New Zealand is President of the Security Council this month but handed the conduct of the poll to Russia because of its interest in Clark's candidacy.
There is another straw poll on September 26 and the Security Report has reported the Council will move to coloured ballot papers for the first time in early October.
Those are more formal votes and it will become clearer which way the permanent five members are voting - and which candidates will be vetoed.
Russia is pushing for an Eastern European candidate.
How they're placed after the fourth round (previous poll placings in brackets):
1. Antonio Guterres, Portugal (1, 1, 1)
2. Miroslav Lajcak, Slovakia (7, 10, 2)
3. Vuk Jeremic, Serbia (4, 2, 3)
4. Srgjan Kerim, Macedonia (5, 6, 6)
5. Irina Bokova, Bulgaria (3, 5, 3)
6. Danilo Turk, Slovenia (2, 4, 8)
7. Susana Malcorra, Argentina (8, 3, 5)
8. Helen Clark, New Zealand (6, 7, 7)
9. Christiana Figueres, Costa Rica (9, 8, 9)
10. Natalia Gherman, Moldova (10, 9, 9)
The following are the actual ratings each candidate got in today's ballot from the three choices, "encourage," "discourage," or "no opinion":
• Antonio Guterres, Portugal: 12 - 2 - 1
• Miroslav Lajcak, Slovakia: 10 - 4 - 1
• Vuk Jeremic, Serbia: 9 - 4 - 2
• Srgjan Kerim, Macedonia: 8 - 7 - 0
• Irina Bokova, Bulgaria: 7 - 5 - 3
• Danilo Turk, Slovenia: 7 - 6 - 2
• Susana Malcorra, Argentina: 7 - 7 - 1
• Helen Clark, New Zealand: 6 - 7 - 2
• Christiana Figueres, Costa Rica: 5 - 10 - 0
• Natalia Gherman, Moldova: 3 - 11 - 1