Ex-Cabinet minister Mel Stride has been knocked out of the contest to succeed Rishi Sunak as Conservative leader.
He failed to make the cut as the contest was narrowed down to four candidates on Tuesday evening.
Votes for the five candidates who had made it through to the second round were:
33 - Former immigration minister Robert Jenrick
28 - Ex-Business Secretary Kemi Badenoch
21 - Ex-Foreign Secretary James Cleverly
21 - Tom Tugendhat
16 - Former Work and Pensions Secretary Mr Stride
The result means the four with the highest number of votes go through to the next stage of the race where the contenders will take part in a series of events at the Tory annual rally in Birmingham which starts at the end of the month.
They will be tested on their abilities to give powerful speeches, to face questions, and to set out policies and a vision for Britain.
Conservative MPs will then stage more votes on October 9 and 10 to draw up a shortlist of two candidates to be put to party members.
The ballot of Party members will be conducted via secure online voting.
It will close at 5pm on Thursday October 31, with the result being announced on Saturday November 2.
Only members who have been a member for 90 days or more prior to the ballot closing, and have been an active member at the time of the nominations for candidates opening, will be eligible to vote.
Earlier on Tuesday morning, Mr Cleverly picked up two new MP backers who went public.
Tory MPs Greg Smith and Sir Alec Shelbrooke supported Dame Priti Patel before her elimination from the contest in the first round and then decided to back Mr Cleverly.
Dozens of Conservative MPs have kept who they are backing secret.
Mr Stride has stressed that the Tory Party must not abandon the Centre ground.
In the first round of voting, Mr Jenrick picked up 28 votes ahead of Ms Badenoch on 22, Mr Cleverly on 21, Mr Tugendhat on 17 and Mr Stride on 16.
Dame Priti was eliminated with 14 votes.
