Updating data in h:inputText field

Question

In my <h:inputText> field, first time user enter a number to search, and the number saved in the session, later on from page to page navigation, sometime user can selected another order number , save the number in session and refresh the whole web content, the value in this <h:inputText> field should update the new number from session everytime the web page reloaded, this actually working fine in the <h:outputText> field as following code <h:outputText value="#{MyPageCode.orderNumber}"/> which getting the orderNumber from session,
but it is not working in the <h:inputText> getting the new number from session, it always keep the first time user entered number there, can someone help me to solve the problem?
Thanks a lot !
<h:form styleClass="form">
  <h:outputText  value="Order#: "/>
     <h:inputText  value="#{mySession.orderNo}">  </h:inputText>
          <f:param name="orderNo" value="#mySession.orderNo}">
          </f:param>
<h:commandLink  style="padding-top:3px;" action="#{myBean.searchAction}">
   <h:outputText  value="Search" >
   </h:outputText>
</h:commandLink>
<h:outputText  value="Order number is#: "/>
<h:outputText value="#{MyPageCode.orderNumber}"/>
</h:form>

Answer 1

Here you are, hope I did not lost anything... Thanks!
faces-config.xml:
====================
<managed-bean>
          <managed-bean-name>mySession</managed-bean-name>
          <managed-bean-class>myManagedSession</managed-bean-class>
          <managed-bean-scope>session</managed-bean-scope>
     </managed-bean>
     <managed-bean>
               <managed-bean-name>myBean</managed-bean-name>
               <managed-bean-class>MyManagedBean</managed-bean-class>
               <managed-bean-scope>request</managed-bean-scope>
     </managed-bean>
     <managed-bean>
               <managed-bean-name>MyPageCode</managed-bean-name>
               <managed-bean-class>MyManagedPageCode</managed-bean-class>
               <managed-bean-scope>request</managed-bean-scope>
     </managed-bean>
     =================================
     public class MySession {
        private Integer orderNo;
             public Integer getOrderNo() {
                  return orderNo;
             public void setOrderNo(Integer orderNo) {
                  this.orderNo = orderNo;
            public void setOrderNumber(int on) {
              // set order number in session
      ===================
       public class MyBean {
     public String searchAction() {
               Integer orderNo = getMySession().getOrderNo();
               if(orderNo != null){               
                  int orderNumber = orderNo.intValue();
                  getRequestScope().put("OrderNumber", new Integer(orderNumber));
                  getMySession().setOrderNumber(orderNumber);                    
               return "page1";
     protected MySession getMySession() {
               if (mySession == null) {
                    mySession = (MySession) getFacesContext()
                              .getApplication().createValueBinding("#{mySession}")
                              .getValue(getFacesContext());
               return mySession;
=========
public class MyPageCode {
    public int  getOrderNumber() {
         // get from session
}