It is the other way around. Meiosis I (or reductional division) splits chromosome _pairs_ so each cell gets half of the chromosomes of the parent. Meiosis II (or equational division) splits double-chromatid chromosomes (making two single-chromatid chromosomes), so cells retain the number of chromosomes, like in mitosis.
* * *
If more clarification needed:
* before the S phase: 23 pairs of chromosomes, 46 single-chromatid chromosomes
* before the meiosis I: 23 pairs of chromosomes, 46 double-chromatid chromosomes
* before the meiosis II: 23 double-chromatid chromosomes without their homologous other
* after the meiosis II: 23 single-chromatid chromosomes without their homologous other
* after fertilization = before the S phase
(I'm talking about humans here.)