Context : L1521E is a dense starless core in Taurus that was found to have relatively low molecular depletion by earlier studies , thus suggesting a recent formation . Aims : We aim to characterize the chemical structure of L1521E and compare it to the more evolved L1544 pre-stellar core . Methods : We have obtained \sim 2.5 \times 2.5 arcminute maps toward L1521E using the IRAM-30m telescope in transitions of various species , including C ^ { 17 } O , CH _ { 3 } OH , c -C _ { 3 } H _ { 2 } , CN , SO , H _ { 2 } CS , and CH _ { 3 } CCH . We derived abundances for the observed species and compared them to those obtained toward L1544 . We estimated CO depletion factors using the C ^ { 17 } O IRAM-30m map , an N ( H _ { 2 } ) map derived from Herschel /SPIRE data and a 1.2 mm dust continuum emission map obtained with the IRAM-30m telescope . Results : Similarly to L1544 , c -C _ { 3 } H _ { 2 } and CH _ { 3 } OH peak at different positions . Most species peak toward the c -C _ { 3 } H _ { 2 } peak : C _ { 2 } S , C _ { 3 } S , HCS ^ { + } , HC _ { 3 } N , H _ { 2 } CS , CH _ { 3 } CCH , C ^ { 34 } S. C ^ { 17 } O and SO peak close to both the c -C _ { 3 } H _ { 2 } and the CH _ { 3 } OH peaks . CN and N _ { 2 } H ^ { + } peak close to the Herschel dust peak . We found evidence of CO depletion toward L1521E . The lower limit of the CO depletion factor derived toward the Herschel dust peak is 4.3 \pm 1.6 , which is about a factor of three lower than toward L1544 . We derived abundances for several species toward the dust peaks of L1521E and L1544 . The abundances of sulfur-bearing molecules such as C _ { 2 } S , HCS ^ { + } , C ^ { 34 } S , C ^ { 33 } S , and SO are higher toward L1521E than toward L1544 by factors of \sim 2-20 , compared to the abundance of A-CH _ { 3 } OH . The abundance of methanol is very similar toward the two cores . Conclusions : The higher abundances of sulfur-bearing species toward L1521E than toward L1544 suggest that significant sulfur depletion takes place during the dynamical evolution of dense cores , from the starless to pre-stellar stage . The CO depletion factor measured toward L1521E suggests that CO is more depleted than previously found . Similar CH _ { 3 } OH abundances between L1521E and L1544 hint that methanol is forming at specific physical conditions in the Taurus Molecular Cloud Complex , characterized by densities of a few \times 10 ^ { 4 } cm ^ { -3 } and N ( H _ { 2 } ) \gtrsim 10 ^ { 22 } cm ^ { -2 } , when CO starts to catastrophically freeze-out , while water can still be significantly photodissociated , so that the surfaces of dust grains become rich in solid CO and CH _ { 3 } OH , as already found toward L1544 . Methanol can thus provide selective crucial information about the transition region between dense cores and the surrounding parent cloud .