Presumably, its primitive name had been Madalena or Santa Maria Madalena.  And later the denomination of “Mar” was added, because it runs along the ocean.  Or maybe “Mar” was added to distinguish it from the site and chapel of Santa Maria Madalena in the parish of Porto do Moniz which became the centre of a well known and well attended pilgrimage.
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The parish originated from a populated farm that was there from the beginning of the colonial period with a chapel and whose saint was Santa Maria Madalena, It was also affirmed that the small primitive church had the invocation of Santa Catarina.
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This parish was dismembered from the Ponta do Sol parish, being established as an independent parish by the bishop D. Jerónimo Barreto on the 1st of February of 1582.  The first parish priest was João Leandro Afonso.
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in Elucidário Madeirense, vol. (F-N), pp. 292-293.