The firm has spent £305,394 in total buying the shares.
Bacanora is Rare Earth's (REM's) joint venture partner on the Sonora lithium project in Mexico and last month REM chairman David Lenigas joined the board at Bacanora as a non-exec director.
REM also has a 30% direct interest in the Fleur - El Sauz and Megalit joint ventures on the property. It means REM now has a total economic interest in each of these ventures of 40.78%.
In February this year Lenigas said REM believed that 2015 would represent a pivotal year for Bacanora.
"The work being carried out on the Sonora Lithium project will, we believe, cement this project as globally significant and one that could service a large proportion of the rapidly increasing lithium market."
REM shares eased 7.23% to 1.09p.
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