<?xml version="1.0" encoding="utf-8"?>
<xs:schema xmlns:link="http://www.xbrl.org/2003/linkbase" xmlns:xbrli="http://www.xbrl.org/2003/instance" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cost="http://costain.com" targetNamespace="http://costain.com" xmlns:xs="http://www.w3.org/2001/XMLSchema">
  <xs:import schemaLocation="http://www.xbrl.org/2003/xbrl-instance-2003-12-31.xsd" namespace="http://www.xbrl.org/2003/instance" />
  <xs:import schemaLocation="http://www.esma.europa.eu/taxonomy/2020-03-16/esef_cor.xsd" namespace="http://www.esma.europa.eu/taxonomy/2020-03-16/esef_cor" />
  <xs:import schemaLocation="http://www.xbrl.org/lrr/arcrole/esma-arcrole-2018-11-21.xsd" namespace="http://www.esma.europa.eu/xbrl/esef/arcrole/wider-narrower" />
  <xs:import schemaLocation="http://www.xbrl.org/2005/xbrldt-2005.xsd" namespace="http://xbrl.org/2005/xbrldt" />
  <xs:annotation>
    <xs:appinfo>
      <link:roleType id="NotesAndMandatoryItems" roleURI="http://costain.com/roles/NotesAndMandatoryItems">
        <link:definition>01 - Notes And Mandatory Items</link:definition>
        <link:usedOn>link:definitionLink</link:usedOn>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:labelLink</link:usedOn>
      </link:roleType>
      <link:linkbaseRef xlink:arcrole="http://www.w3.org/1999/xlink/properties/linkbase" xlink:href="cost-2021-12-31_lab-en.xml" xlink:role="http://www.xbrl.org/2003/role/labelLinkbaseRef" xlink:type="simple" />
      <link:linkbaseRef xlink:arcrole="http://www.w3.org/1999/xlink/properties/linkbase" xlink:href="cost-2021-12-31_pre.xml" xlink:role="http://www.xbrl.org/2003/role/presentationLinkbaseRef" xlink:type="simple" />
      <link:linkbaseRef xlink:arcrole="http://www.w3.org/1999/xlink/properties/linkbase" xlink:href="cost-2021-12-31_def.xml" xlink:role="http://www.xbrl.org/2003/role/definitionLinkbaseRef" xlink:type="simple" />
      <link:linkbaseRef xlink:arcrole="http://www.w3.org/1999/xlink/properties/linkbase" xlink:href="cost-2021-12-31_cal.xml" xlink:role="http://www.xbrl.org/2003/role/calculationLinkbaseRef" xlink:type="simple" />
      <link:linkbaseRef xlink:arcrole="http://www.w3.org/1999/xlink/properties/linkbase" xlink:href="http://www.esma.europa.eu/taxonomy/2020-03-16/esef_cor-lab-en.xml" xlink:role="http://www.xbrl.org/2003/role/labelLinkbaseRef" xlink:type="simple" />
      <link:linkbaseRef xlink:arcrole="http://www.w3.org/1999/xlink/properties/linkbase" xlink:href="http://www.esma.europa.eu/taxonomy/2020-03-16/esef_cor-gen-en.xml" xlink:type="simple" />
      <link:roleType id="Anchoring" roleURI="http://costain.com/roles/Anchoring">
        <link:definition>99 - Groups all anchored elements</link:definition>
        <link:usedOn>link:definitionLink</link:usedOn>
        <link:usedOn>link:labelLink</link:usedOn>
      </link:roleType>
      <link:roleType id="ProfitOrLoss" roleURI="http://costain.com/roles/ProfitOrLoss">
        <link:definition>02 - Profit or loss</link:definition>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:labelLink</link:usedOn>
      </link:roleType>
      <link:roleType id="StatementOfComprehensiveIncome" roleURI="http://costain.com/roles/StatementOfComprehensiveIncome">
        <link:definition>03 - Statement of comprehensive income</link:definition>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:labelLink</link:usedOn>
      </link:roleType>
      <link:roleType id="StatementOfFinancialPosition" roleURI="http://costain.com/roles/StatementOfFinancialPosition">
        <link:definition>04 - Statement of financial position</link:definition>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:labelLink</link:usedOn>
      </link:roleType>
      <link:roleType id="StatementOfChangesInEquity" roleURI="http://costain.com/roles/StatementOfChangesInEquity">
        <link:definition>05 - Statement of changes in equity</link:definition>
        <link:usedOn>link:definitionLink</link:usedOn>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:labelLink</link:usedOn>
      </link:roleType>
      <link:roleType id="StatementOfCashFlows" roleURI="http://costain.com/roles/StatementOfCashFlows">
        <link:definition>06 - Statement of cash flows</link:definition>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:labelLink</link:usedOn>
      </link:roleType>
    </xs:appinfo>
  </xs:annotation>
  <xs:element id="COST_LossFromOperations" xbrli:balance="debit" xbrli:periodType="duration" name="LossFromOperations" nillable="true" substitutionGroup="xbrli:item" type="xbrli:monetaryItemType" />
</xs:schema>